First-passage exponents of multiple random walks

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 49, 2010, Pages

  Ben Naim, E ^a   Krapivsky, P L ^b  

^a CENTER FOR NONLINEAR STUDIES   (United States)

^b Boston University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78649718443     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/49/495008     Document Type: Article

References (54)

1. Feller W 1968 An Introduction to Probability Theory and Its Applications vol I (New York: Wiley)
2. Weiss G H 1994 Aspects and Applications of the Random Walk (Amsterdam: North-Holland)
3. Berg H C 1983 Random Walks in Biology (Princeton, NJ: Princeton University Press)
4. Rudnick J and Gaspari G 2004 Elements of the Random Walk: An Introduction for Advanced Students and Researchers (New York: Cambridge University Press)
5. Fisher M E 1984 J. Stat. Phys. 34 667
6. Huse D A and Fisher M E 1984 Phys. Rev. B 29 239
7. Wei Q H, Bechinger C and Leiderer P 2000 Science 287 625
8. Cui B X, Diamant H and Lin B H 2002 Phys. Rev. Lett. 89 188302
9. Lee B P 1994 J. Phys. A: Math. Gen. 27 2633
10. Redner S 2001 A Guide to First-Passage Processes (New York: Cambridge University Press)
11. Derrida B, Hakim V and Pasquier V 1995 Phys. Rev. Lett. 75 751
12. Majumdar S N 1999 Curr. Sci. 77 370
13. Niederhausen H 1983 Eur. J. Comb. 4 161
14. Ben-Naim E, Daya Z A, Vorobieff P and Ecke R E 2001 Phys. Rev. Lett. 86 1414
15. Fisher M E and Gelfand M P 1988 J. Stat. Phys. 53 175
16. Bramson M and Griffeath D 1991 Random Walks, Brownian Motion and Interacting Particle Systems: A Festshrift in Honor of Frank Spitzer ed R Durrett and H Kesten (Boston, MA: Birkhäuser)
17. Grabiner D J 1999 Ann. Inst. Poincare: Prob. Stat. 35 177
18. Krapivsky P L and Redner S 1996 J. Phys. A: Math. Gen. 29 5347
19. Redner S and Krapivsky P L 1999 Am. J. Phys. 67 1277
20. Ben-Avraham D, Johnson BM,Monaco C A, Krapivsky P L and Redner S 2003 J. Phys. A: Math. Gen. 36 1789
21. Cardy J and Katori M 2003 J. Phys. A: Math. Gen. 36 609
22. Burkholder D L 1977 Adv. Math. 26 182
23. Yuste S B, Acedo L and Lindenberg K 2001 Phys. Rev. E 64 052102
24. Yuste S B and Acedo L 2001 Phys. Rev. E 64 061107
25. Yuste S B and Acedo L 2001 Physica A 297 321
26. Barenblatt G I 1996 Scaling, Self-Similarity and Intermediate Asymptotics (Cambridge: Cambridge University Press)
27. Stanley H E 1971 Introduction to Phase Transitions and Critical Phenomena (New York: Oxford University Press)
28. Ben-Naim E and Krapivsky P L 2010 J. Phys. A: Math. Theor. 43 495007
29. Harris T E 1965 J. Appl. Prob. 2 323
30. Levitt D G 1973 Phys. Rev. A 6 3050
31. Alexander S and Pincus P 1978 Phys. Rev. B 18 2011
32. Van Beijeren H, Kehr K W and Kutner R 1983 Phys. Rev. B 28 5711
33. Tracy C A and Widom H 1994 Commun. Math. Phys. 159 151
34. Arratia R 1983 Ann. Probab. 11 362
35. Krapivsky P L, Redner S and Ben-Naim E 2010 A Kinetic View of Statistical Physics (Cambridge: Cambridge University Press)
36. DeBlassie R D 1987 Probab. Theory Relat. Fields 74 1
37. DeBlassie R D 1988 Probab. Theory Relat. Fields 79 95
38. Bañuelos R and Smiths R G 1997 Probab. Theory Relat. Fields 108 299
39. Olver F W J et al (ed) NIST Handbook of Mathematical Functions (Cambridge: Cambridge University Press)
40. Ben-Naim E and Hengartner N W 2007 Phys. Rev. E 76 026106
41. Ben-Avraham D, Majumdar S N and Redner S 2007 J. Stat. Mech. L04002
42. Antal T, Ben-Naim E and Krapivsky P L 2010 J. Stat. Mech. P07009
43. Carslaw H S and Jaeger J C 1959 Conduction of Heat in Solids (Oxford: Clarendon)
44. Jackson J D 1998 Classical Electrodynamics (New York: Wiley)
45. Varopoulos N Th 1999 Math. Proc. Camb. Phil. Soc. 125 335
46. Varopoulos N Th 1999 Math. Proc. Camb. Phil. Soc. 129 301
47. Davis L C and Reitz J 1975 J. Math. Phys. 16 1219
48. Rayleigh J W S 1877 The Theory of Sound (New York: Macmillan)
49. Rayleigh J W S 1945 The Theory of Sound (New York: Dover) (reprinted)
50. Courant R and Hilbert D 1953 Methods of Mathematical Physics vol I (New York: Wiley)
51. Chavel I 1984 Eigenvalues in Riemannian Geometry (Orlando, FL: Academic)
52. Ben-Avraham D 1988 J. Chem. Phys. 88 941
53. Grassberger P 2002 Comput. Phys. Commun. 147 64
54. Oppelstrup T, Bulatov V V, Donev A, Kalos M H, Gilmer G H and Sadigh B 2009 Phys. Rev. E 80 066701