Probability and real trees

Lecture Notes in Mathematics

Volumn 1920, Issue , 2008, Pages 1-192

  Evans, Steven N ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34948880628     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-74798-7     Document Type: Review

References (149)

1. Romain Abraham and Laurent Serlet. Poisson snake and fragmentation. Electron. J. Probab., 7:no. 17, 15 pp. (electronic), 2002.
2. S. Albeverio and X. Zhao. On the relation between different constructions of random walks on p-adics. Markov Process. Related Fields, 6(2):239-255, 2000.
3. Sergio Albeverio. Theory of Dirichlet forms and applications. In Lectures on probability theory and statistics (Saint-Flour, 2000), volume 1816 of Lecture Notes in Math., pages 1-106. Springer, Berlin, 2003.
4. Sergio Albeverio and Witold Karwowski. Diffusion on p-adic numbers. In Gaussian random, fields (Nagoya, 1990), volume 1 of Ser. Probab. Statist., pages 86-99. World Sci. Publ., River Edge, NJ, 1991.
5. Sergio Albeverio and Witold Karwowski. A random walk on p-adics - the generator and its spectrum. Stochastic Process. Appl., 53(1):1-22, 1994.
6. Sergio Albeverio and Witold Karwowski. Real time random walks on p-adic numbers. In Mathematical physics and stochastic analysis (Lisbon, 1998), pages 54-67. World Sci. Publ., River Edge, NJ, 2000.
7. Sergio Albeverio, Witold Karwowski, and Xuelei Zhao. Asymptotics and spectral results for random walks on p-adics. Stochastic Process. Appl., 83(1):39-59, 1999.
8. Sergio Albeverio and Xuelei Zhao. A decomposition theorem for Lévy processes on local fields. J. Theoret. Probab., 14(1):1-19, 2001.
9. Sergio Albeverio and Xuelei Zhao. A remark on nonsymmetric stochastic processes on p-adics. Stochastic Anal. Appl., 20(2):243-261, 2002.
10. D. Aldous. The continuum random tree III. Ann. Probab., 21:248-289, 1993.
11. D. J. Aldous. Exchangeability and related topics. In École d'été de probabilités de Saint Flour, XIII 1983, volume 1117 of Lecture Notes in Math., pages 1-198. Springer, Berlin - New York, 1985.
12. David Aldous. The continuum random tree I. Ann. Probab., 19:1-28, 1991.
13. David Aldous. The continuum random tree. II. An overview. In Stochastic analysis (Durham, 1990), volume 167 of London Math. Soc. Lecture Note Ser., pages 23-70. Cambridge Univ. Press, Cambridge, 1991.
14. David Aldous. Tree-valued Markov chains and Poisson-Galton-Watson distributions. In Micro-surveys in discrete probability (Princeton, NJ, 1997), volume 41 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pages 1-20. Amer. Math. Soc., Providence, RI, 1998.
15. David Aldous and Steven N. Evans. Dirichlet forms on totally disconnected spaces and bipartite Markov chains. J. Theoret. Probab., 12(3):839-857, 1999.
16. David Aldous and Jim Pitman. Tree-valued Markov chains derived from Galton-Watson processes. Ann. Inst. H. Poincaré Probab. Statist., 34(5):637-686, 1998.
17. David J. Aldous. The random walk construction of uniform spanning trees and uniform labelled trees. SIAM J. Discrete Math., 3(4):450-465, 1990.
18. D.J. Aldous. Deterministic and stochastic models for coalescence (aggregation, coagulation): a review of the mean field theory for probabilists. Bernoulli, 5:3-48, 1999.
19. Benjamin L. Allen and Mike Steel. Subtree transfer operations and their induced metrics on evolutionary trees. Ann. Comb., 5(1):1-15, 2001.
20. J.M. Alonso, T. Brady, D. Cooper, V. Ferlini, M. Lustig, M. Mihalik, M. Shapiro, and H. Short. Notes on word hyperbolic groups. In H. Short, editor, Group theory from a geometrical viewpoint (Trieste, 1990), pages 3-63. World Sci. Publishing, River Edge, NJ, 1991.
21. V. Anantharam and P. Tsoucas. A proof of the Markov chain tree theorem. Statist Probab. Lett., 8(2):189-192, 1989.
22. R. A. Arratia. Coalescing Brownian motions on the line. PhD thesis, University of Wisconsin-Madison, 1979.
23. S. Asmussen and T. G. Kurtz. Necessary and sufficient conditions for complete convergence in the law of large numbers. Ann. Probab., 8(1):176-182, 1980.
24. Martin T. Barlow and Steven N. Evans. Markov processes on vermiculated spaces. In Random walks and geometry, pages 337-348. Walter de Gruyter GmbH & Co. KG, Berlin, 2004.
25. M.T. Barlow, M. Émery, F.B. Knight, S. Song, and M. Yor. Autour d'un théorème de Tsirelson sur les filtrations browniennes et non browniennes. In Séminaire de Probabilités, XXXII, volume 1686 of Lecture Notes in Mathematics, pages 264-305. Springer, Berlin, 1998.
26. M.T. Barlow, J. Pitman, and M. Yor. On Walsh's Brownian motions. In Séminaire de Probabilités, XXXII, volume 1372 of Lecture Notes in Mathematics, pages 275-293. Springer, Berlin, New York, 1989.
27. I. Benjamini and Y. Peres. Random walks on a tree and capacity in the interval. Ann. Inst. II. Poincaré Probab. Statist., 28:557-592, 1992.
28. Julien Berestycki, Nathanael Berestycki, and Jason Schweinsberg. Betacoalescents and continuous stable random trees.
29. Jean Bertoin. Lévy processes, volume 121 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1996.
30. Mladen Bestvina. ℝ-trees in topology, geometry, and group theory. In Handbook of geometric topology, pages 55-91. North-Holland, Amsterdam, 2002.
31. Philippe Biane, Jim Pitman, and Marc Yor. Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions. Bull. Amer. Math. Soc. (N.S.), 38(4):435-465 (electronic), 2001.
32. 1. Ann. Probab., 8:183-213, 1980.
33. Martin R. Bridson and André Haefliger. Metric spaces of non-positive curvature, volume 319 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 1999.
34. Martin R. Bridson and Andre Haeflinger. Metric Spaces and Non-Positive Curvature. Springer, 2001.
35. A. Broder. Generating random spanning trees. In Proc. 30'th IEEE Symp. Found. Comp. Sci., pages 442-447, 1989.
36. Peter Buneman. A note on the metric properties of trees. J. Combinatorial Theory Ser. B, 17:48-50, 1974.
37. Dmitri Burago, Yuri Burago, and Sergei Ivanov. A course in metric geometry, volume 33 of Graduate studies in mathematics. AMS, Boston, MA, 2001.
38. P. Cartier. Fonctions harmoniques sur un arbre. In Convegno di Calcolo delle Probabilità, INDAM, Rome, 1971, volume IX of Symposia Mathematica, pages 203-270. Academic Press, London, 1972.
39. Ian Chiswell. Introduction to A-trees. World Scientific Publishing Co. Inc., River Edge, NJ, 2001.
40. M. Coornaert, T. Delzant, and A. Papadopoulos. Géométrie et théorie des groupes, volume 1441 of Lecture Notes in Mathematics. Springer, 1990.
41. D. J. Daley and D. Vere-Jones. An introduction to the theory of point processes. Springer Series in Statistics. Springer-Verlag, New York, 1988.
42. D.S. Dean and K.M. Jansons. Brownian excursions on combs. J. Statist. Phys., 70:1313-1332, 1993.
43. Claude Dellacherie and Paul-André Meyer. Probabilities and potential. C, volume 151 of North-Holland Mathematics Studies. North-Holland Publishing Co., Amsterdam, 1988. Potential theory for discrete and continuous semi-groups, Translated from the French by J. Norris.
44. Peter Donnelly, Steven N. Evans, Klaus Fleischmann, Thomas G. Kurtz, and Xiaowen Zhou. Continuum-sites stepping-stone models, coalescing exchangeable partitions and random trees. Ann. Probab., 28(3): 1063-1110, 2000.
45. Andreas Dress, Vincent Moulton, and Werner Terhalle. T-theory: an overview. European J. Combin., 17(2-3):161-175, 1996. Discrete metric spaces (Bielefeld, 1994).
46. Andreas W.M. Dress. Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorical properties of metric spaces. Adv. Math., 53:321-402, 1984.
47. A.W. Dress and W.F. Terhalle. The real tree. Adv. Math., 120:283-301, 1996.
48. R.M. Dudley. Real Analysis and Probability. Wadsworth, Belmont CA, 1989.
49. Thomas Duquesne and Jean-François Le Gall. Probabilistic and fractal aspects of Lévy trees. Probab. Theory Related Fields, 131(4):553-603, 2005.
50. Thomas Duquesne and Matthias Winkel. Growth of Levy trees.
51. E.B. Dynkin. Integral representations of excessive measures and excessive functions. Russian Math. Surveys, 27:43-84, 1972.
52. E.B. Dynkin and M.B. Malyutov. Random walk on groups with a finite number of generators (Russian). Dokl. Akad. Nauk SSSR, 137:1042-1045, 1961.
53. N. Eisenbaum and H. Kaspi. A counterexample for the Markov property of local time for diffusions on graphs. In Séminaire de Probabilités, XXIX, volume 1613 of Lecture Notes in Mathematics, pages 260-265. Springer, Berlin, 1995.
54. N. Eisenbaum and H. Kaspi. On the Markov property of local time for Markov processes on graphs. Stochastic Process. Appl., 64:153-172, 1996.
55. Alexei Ermakov, Bálint Töth, and Wendelin Werner. On some annihilating and coalescing systems. J. Statist. Phys., 91(5-6):845-870, 1998.
56. S.N. Ethier and T.G. Kurtz. Markov Processes: Characterization and Convergence. Wiley, New York, 1986.
57. Stewart N. Ethier and Thomas G. Kurtz. Markov processes. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons Inc., New York, 1986. Characterization and convergence.
58. S.N. Evans. Local field Gaussian measures. In E. Cinlar, K.L. Chung, and R.K. Getoor, editors, Seminar on Stochastic Processes, 1988 (Gainesville, FL, 1988), pages 121-160. Birkhäuser, Boston, 1989.
59. S.N. Evans. Local properties of Lévy processes on a totally disconnected group. J. Theoret. Probab., 2:209-259, 1989.
60. Steven N. Evans. Kingman's coalescent as a random metric space. In Stochastic models (Ottawa, ON, 1998), volume 26 of CMS Conf. Proc., pages 105-114. Amer. Math. Soc., Providence, RI, 2000.
61. Steven N. Evans. Snakes and spiders: Brownian motion on R-trees. Probab. Theory Rel. Fields, 117:361-386, 2000.
62. Steven N. Evans. Local fields, Gaussian measures, and Brownian motions. In Topics in probability and Lie groups: boundary theory, volume 28 of CRM Proc. Lecture Notes, pages 11-50. Amer. Math. Soc., Providence, RI, 2001.
63. Steven N. Evans, Jim Pitman, and Anita Winter. Rayleigh processes, real trees, and root growth with re-grafting. Probab. Theory Related Fields, 134(1):81-126, 2006.
64. Steven N. Evans and Richard B. Sowers. Pinching and twisting Markov processes. Ann. Probab., 31(1):486-527, 2003.
65. Steven N. Evans and Anita Winter. Subtree prune and regraft: a reversible real tree-valued Markov process. Ann. Probab., 34(3):918-961, 2006.
66. W. Feller. An Introduction to Probability Theory and Its Applications, volume II. Wiley, New York, 2nd edition, 1971.
67. Joseph Felsenstein. Inferring Phytogenies. Sinauer Associates, Sunderland, Massachusetts, 2003.
68. A. Figa-Talamanca. Diffusion on compact ultrametric spaces. In Noncompact Lie Groups and some of their Applications (San Antonio, TX, 1993), pages 157-167. Kluwer, Dordrecht, 1994,
69. Peter Forster and Colin Renfrew, editors. Phylogenetic methods and the prehistory of languages. McDonald Institute for Archaeological Research, Cambridge, 2006.
70. D. Freedman. Brownian Motion and Diffusion. Springer, New York, 1983.
71. M.I. Freidlin and A.D. Wentzell. Diffusion processes on graphs and the averaging principle. Ann. Probab., 21:2215-2245, 1993.
72. Masatoshi Fukushima, Yōichi Ōshima, and Masayoshi Takeda. Dirichlet forms and symmetric Markov processes, volume 19 of de Gruyter Studies in Mathematics. Walter de Gruyter & Co., Berlin, 1994.
73. M.A. Garcia Alvarez. Une théorie de la dualité à ensemble polaire près II. Ann. Probab., 4:947-976, 1976.
74. M.A. Garcia Alvarez and P.A. Meyer. Une théorie de la dualité à ensemble polaire près I. Ann. Probab., 1:207-222, 1973.
75. R.K. Getoor and J. Glover. Markov processes with identical excessive measures. Math. Z., 184:287-300, 1983.
76. E. Ghys and P. de la Harpe, editors. Sur les groupes hyperboliques d'apres Mikhael Gromov: papers from the Swiss seminar on hyperbolic groups held in Bern, 1988, volume 83 of Progress in Mathematics. Birkhäuser, Boston, MA, 1990.
77. Stephen Jay Gould. Dinosaur in a haystack: reflections in natural history. Harmony Books, New York, 1995.
78. Andreas Greven, Peter Pfaffelhuber, and Anita Winter. Convergence in distribution of random metric measure spaces: (Λ-coalescent measure trees).
79. M. Gromov. Hyperbolic groups. In Essays in group theory, volume 8 of Math. Sci. Res. Inst. Publ., pages 75-263. Springer, New York, 1987.
80. Misha Gromov. Metric structures for Riemannian and non-Riemannian spaces, volume 152 of Progress in Mathematics. Birkhäuser Boston Inc., Boston, MA, 1999. Based on the 1981 French original [MR 85e:53051], With appendices by M. Katz, P. Pansu and S. Semmes, Translated from the French by Sean Michael Bates.
81. Benedicte Haas, Gregory Miermont, Jim Pitman, and Matthias Winkel. Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models.
82. J. Hawkes. Trees generated by a simple branching process. J. London Math. Soc. (2), 24:374-384, 1981.
83. Jot un Hein, Mikkel H. Schierup, and Carsten Wiuf. Gene genealogies, variation and evolution. Oxford University Press, Oxford, 2005. A. primer in coalescent theory.
84. Julia Heinonen and Stephen Semmes. Thirty-three yes or no questions about mappings, measures, and metrics. Conform. Geom. Dyn., 1:1-12 (electronic), 1997.
85. J.G. Hocking and G.S. Young. Topology. Addison-Wesley, Reading, MA, 1961.
86. T. Jeulin, Compactification de Martin d'un processus droit. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 42:229-260, 1978.
87. p induced by maps and recurrence criteria. Forum Math., 16(1):69-95, 2004.
88. John L. Kelley. General topology. Springer-Verlag, New York, 1975. Reprint of the 1955 edition [Van Nostrand, Toronto, Out.], Graduate Texts in Mathematics, No. 27.
89. J.F.C. Kingman. On the genealogy of large populations. In J. Gani and E.J. Hannan, editors, Essays in Statistical Science, pages 27-43. Applied Probability Trust, 1982. Special vol. 19A of J. Appl. Probab.
90. J.F.C. Kingman. The coalescent. Stochastic Process. Appl., 13:235-248, 1982.
91. F.B. Knight. Essentials of Brownian Motion and Diffusion, volume 18 of Mathematical Surveys and Monographs. American Mathematical. Society, Providence, 1981.
92. Frank B. Knight. Essentials of Brownian motion and diffusion, volume 18 of Mathematical Surveys. American Mathematical Society, Providence, R.I., 1981.
93. W.B. Krebs. Brownian motion on the continuum tree. Probab. Theory Related Fields, 101:421-433, 1995.
94. H. Kunita and T. Watanabe. Markov processes and Martin boundaries, I. Illinois J. Math., 9:485-526, 1965.
95. T. J. Laakso. Ahlfors Q-regular spaces with arbitrary Q > 1 admitting weak Poincaré inequality. Geom. Funct. Anal., 10(1):111-123, 2000.
96. Steven P. Lalley and Thomas Sellke. An extension of Hawkes' theorem on the Hausdorff dimension of a Galton-Watson, tree. Probab. Theory Related Fields, 116(1):41-56, 2000.
97. J.-F. Le Gall. A class of path-valued Markov processes and its applications to superprocesses. Probab. Theory Related Fields, 95:25-46, 1993.
98. J.-F. Le Gall. A path-valued Markov process and its connections with partial differential equations. In First European Congress of Mathematics, Vol. II (Paris, 1992), volume 120 of Progr. Math., pages 185-212. Birkhuser, Basel, 1994.
99. J.-F. Le Gall. Hitting probabilities and potential theory for the Brownian path-valued process. Ann. Inst. Fourier (Grenoble), 44:277-306, 1994.
100. 2 in a domain. Probab. Theory Related Fields, 102:393-432, 1995.
101. Jean-François Le Gall. Random trees and applications. Probab. Surv., 2:245-311 (electronic), 2005.
102. Jean-François Le Gall. Random real, trees. Ann. Fac. Sci. Toulouse Math. (6), 15(1):35-62, 2006.
103. Jean-François Le Gall and Mathilde Weill. Conditioned Brownian trees. Ann. Inst. H. Poincaré Probab. Statist., 42(4):455-489, 2006.
104. R.D. Lyons. Random walks and percolation on trees. Ann. Probab., 18:931-958, 1990.
105. R.D. Lyons and Y. Peres. Probability on trees and networks. Book in preparation for Cambridge University Press, available via http://php.indiana. edu/~rdlyons/, 1996.
106. Z.-M. Ma and M. Röckner. Introduction to the Theory of (Non-Symmetric) Dirichlet Forms. Springer, Berlin, 1992.
107. P. Mattila. Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, volume 44 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge-New York, 1995.
108. P.-A. Meyer. Processus de Markov: la Frontière de Martin, volume 77 of Lecture Notes in Mathematics. Springer, Berlin, 1970.
109. M. Mezard, G. Parisi, and M.A. Virasoro. Spin Glass Theory and Beyond, volume 9 of World Scientific Lecture Notes in Physics. World Scientific, Singapore, 1987.
110. John W. Morgan. Λ-trees and their applications. Bull. Amer. Math. Soc. (NS.), 26(1):87-112, 1992.
111. Natella V. O'Bryant. A noisy system, with a flattened Hamiltonian and multiple time scales. Stoch. Dyn., 3(1): 1-54, 2003.
112. R. Pemantle and Y. Peres. Galton-Watson trees with the same mean have the same polar sets. Ann. Probab., 23:1102-1124, 1995.
113. R. Pemantle, Y. Peres, and J. W. Shapiro. The trace of spatial Brownian motion is capacity equivalent to the unit square. Probab. Theory Related Fields, 106:379-399, 1996.
114. Y. Peres. Remarks on intersection-equivalence and capacity-equivalence. Ann. Inst. II. Poincaré Phys. Théor., 64:339-347, 1996.
115. J. Pitman. Combinatorial stochastic processes, volume 1875 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2006. Lectures from the 32nd Summer School on Probability Theory held in Saint-Flour, July 7-24, 2002, With a foreword by Jean Picard.
116. Jim Pitman. Coalescents with multiple collisions. Ann. Probab., 27(4):1870-1902, 1999.
117. Daniel Revuz and Marc Yor. Continuous martingales and Brownian motion, volume 293 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, third edition, 1999.
118. D. Ringe, T. Warnow, and A. Taylor. Indo-European and computational cladistics. Transactions of the Philological Society, 100:59-129, 2002.
119. L. C. G. Rogers and David Williams. Diffusions, Markov processes, and martingales. Vol. 2. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2000. Itô calculus, Reprint of the second (1994) edition.
120. L.C.G. Rogers and D. Williams. Diffusions, Markov Processes, and Martingales, Volume I: Foundations. Wiley, 2nd edition, 1994.
121. H. L. Royden. Real Analysis. Collier MacMillan - New York, 2nd edition, 1968.
122. S. Sawyer. Isotropic random walks in a tree. Z. Wahrsch. Verw. Gebiete, 42:279-292, 1978.
123. W. H. Schikhof. Ultrametric Calculus: an Introduction to p-adic Analysis, volume 4 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge - New York, 1984.
124. D. Schwartz. On hitting probabilities for an annihilating particle model. Ann. Probab., 6:398-403, 1976.
125. Charles Semple and Mike Steel. Phylogenetics, volume 24 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford, 2003.
126. Peter B. Shalen. Dendrology of groups: an introduction, In Essays in group theory, volume 8 of Math. Sci. Res. Inst. Publ., pages 265-319. Springer, New York, 1987.
127. Peter B. Shalen. Dendrology and its applications. In Group theory from a geometrical viewpoint (Trieste, 1990), pages 543-616. World Sci. Publishing, River Edge, NJ, 1991.
128. M. Sharpe. General Theory of Markov Processes. Academic Press, San Diego, 1988.
129. G.F. Simmons. Introduction to Topology and Modern Analysis. McGraw-Hill, New York, 1963.
130. J. M. S. Simões Pereira, A note on the tree realizability of a distance matrix. J. Combinatorial Theory, 6:303-310, 1969.
131. Li Song, Li Jiao, and Xue Lei Zhao. Some time estimates of Lévy processes on p-adics. J. Fudan Univ. Nat. Sci., 44(3):457-461, 476, 2005.
132. Florin Soucaliuc, Bálint Tóth, and Wendelin Werner. Reflection and coalescence between independent one-dimensional Brownian paths. Ann. Inst. H. Poincaré Probab. Statist., 36(4):509-545, 2000.
133. Richard B. Sowers. Stochastic averaging with a flattened Hamiltonian: a Markov process on a stratified space (a whiskered sphere). Trans. Amer. Math. Soc., 354(3):853-900 (electronic), 2002.
134. D.L. Swofford and G.J. Olsen. Phylogeny reconstruction. In D.M. Hillis and C. Moritz, editors, Molecular Systematics, pages 411-501. Sinauer Associates, Sunderland, Massachusetts, 1990.
135. M.H. Taibleson. Fourier Analysis on Local Fields. Princeton University Press, Princeton, N.J., 1975.
136. S. Tavaré. Line-of-descent and genealogical processes, and their applications in population genetics. Theoret. Population Biol., 26:119-164, 1984.
137. W.F. Terhalle. ℝ-trees and symmetric differences of sets. European J. Combin., 18:825-833, 1997.
138. Bálint Tóth and Wendelin Werner. The true self-repelling motion. Probab. Theory Related Fields, 111(3):375-452, 1998.
139. B. Tsirelson. Triple points: from non-brownian filtrations to harmonic measures. Geom. Fund. Anal., 7:1096-1142, 1997.
140. B. Tsirelson. Brownian coalescence as a black noise I. Preprint, School of Mathematics, Tel Aviv University, 1998.
141. N.T. Varopoulos. Long range estimates for Markov chains. Bull. Sc. Math., 109:225-252, 1985.
142. J.B. Walsh. A diffusion with discontinuous local time. In Temps Locaux, Astérisque, volume 52-53. Société Mathématique de France, Paris, 1978.
143. G.N. Watson. A treatise on the theory of Bessel functions. Cambridge University Press, Cambridge, second edition, 1944.
144. G. A. Watterson. Lines of descent and the coalescent. Theoret. Population Biol., 26:77-92, 1984.
145. W. Woess. Random walks on infinite graphs and groups - a survey of selected topics. Bull. London Math. Soc., 26:1-60, 1994.
146. Lorenzo Zambotti. A reflected stochastic heat equation as symmetric dynamics with respect to the 3-d Bessel bridge. J. Funct. Anal., 180(1):195-209, 2001.
147. Lorenzo Zambotti. Integration by parts on Bessel bridges and related stochastic partial, differential equations. C. R. Math. Acad. Sci Paris, 334(3):209-212, 2002.
148. Lorenzo Zambotti. Integration by parts on δ-Bessel bridges, δ > 3 and related SPDEs. Ann. Probab., 31(1):323-348, 2003.
149. K. A. Zareckiǐ. Constructing a tree on the basis of a set of distances between the hanging vertices. Uspehi Mat. Nauk, 20(6):90-92, 1965.