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Volumn 16, Issue , 2011, Pages 129-136

The growth constants of lattice trees and lattice animals in high dimensions

Author keywords

Growth constant; Lattice animal; Lattice tree; Mean field model

Indexed keywords


EID: 79952822509     PISSN: None     EISSN: 1083589X     Source Type: Journal    
DOI: 10.1214/ECP.v16-1612     Document Type: Article
Times cited : (22)

References (20)
  • 2
    • 34548217153 scopus 로고    scopus 로고
    • Self-avoiding walk enumeration via the lace expansion
    • N. Clisby, R. Liang, and G. Slade. Self-avoiding walk enumeration via the lace expansion. J. Phys. A: Math. Theor., 40:10973-11017, (2007).
    • (2007) J. Phys. A: Math. Theor. , vol.40 , pp. 10973-11017
    • Clisby, N.1    Liang, R.2    Slade, G.3
  • 3
    • 0032362767 scopus 로고    scopus 로고
    • The scaling limit of lattice trees in high dimensions
    • E. Derbez and G. Slade. The scaling limit of lattice trees in high dimensions. Commun. Math. Phys., 193:69-104, (1998).
    • (1998) Commun. Math. Phys. , vol.193 , pp. 69-104
    • Derbez, E.1    Slade, G.2
  • 4
    • 0039004001 scopus 로고    scopus 로고
    • 1/d-expansions for the free energy of weakly embedded site animal models of branched polymers
    • D.S. Gaunt and P. J. Peard. 1/d-expansions for the free energy of weakly embedded site animal models of branched polymers. J. Phys. A: Math. Gen., 33:7515-7539, (2000).
    • (2000) J. Phys. A: Math. Gen. , vol.33 , pp. 7515-7539
    • Gaunt, D.S.1    Peard, P.J.2
  • 5
    • 77952894235 scopus 로고    scopus 로고
    • Borel-type bounds for the self-avoiding walk connective constant
    • B.T. Graham. Borel-type bounds for the self-avoiding walk connective constant. J. Phys. A: Math. Theor., 43:235001, (2010).
    • (2010) J. Phys. A: Math. Theor. , pp. 43
    • Graham, B.T.1
  • 6
    • 50249118414 scopus 로고    scopus 로고
    • Decay of correlations in nearest-neighbor self-avoiding walk, percolation, lattice trees and animals
    • T. Hara. Decay of correlations in nearest-neighbor self-avoiding walk, percolation, lattice trees and animals. Ann. Probab., 36:530-593, (2008).
    • (2008) Ann. Probab. , vol.36 , pp. 530-593
    • Hara, T.1
  • 7
    • 5544254271 scopus 로고
    • On the upper critical dimension of lattice trees and lattice animals
    • T. Hara and G. Slade. On the upper critical dimension of lattice trees and lattice animals. J. Stat. Phys., 59:1469-1510, (1990).
    • (1990) J. Stat. Phys. , vol.59 , pp. 1469-1510
    • Hara, T.1    Slade, G.2
  • 8
    • 84974065206 scopus 로고
    • The self-avoiding-walk and percolation critical points in high dimensions
    • T. Hara and G. Slade. The self-avoiding-walk and percolation critical points in high dimensions. Combin. Probab. Comput., 4:197-215, (1995).
    • (1995) Combin. Probab. Comput. , vol.4 , pp. 197-215
    • Hara, T.1    Slade, G.2
  • 9
    • 0000932430 scopus 로고
    • Renormalized (1/ct) expansion for lattice trees and localization
    • A.B. Harris. Renormalized (1/ct) expansion for lattice trees and localization. Phys. Rev. B, 26:337-366, (1982).
    • (1982) Phys. Rev. B , vol.26 , pp. 337-366
    • Harris, A.B.1
  • 10
    • 21644483183 scopus 로고    scopus 로고
    • Critical points for spread-out self-avoiding walk, percolation and the contact process
    • R. van der Hofstad and A. Sakai. Critical points for spread-out self-avoiding walk, percolation and the contact process. Probab. Theory Related Fields, 132:438-470, (2005).
    • (2005) Probab. Theory Related Fields , vol.132 , pp. 438-470
    • Van Der Hofstad, R.1    Sakai, A.2
  • 11
    • 33746595810 scopus 로고    scopus 로고
    • Expansion in n−1 for percolation critical values on the n-cube and Zn: The first three terms
    • n: the first three terms. Combin. Probab. Comput., 15:695-713, (2006).
    • (2006) Combin. Probab. Comput. , vol.15 , pp. 695-713
    • Van Der Hofstad, R.1    Slade, G.2
  • 12
    • 43449097209 scopus 로고    scopus 로고
    • Convergence of lattice trees to super-Brownian motion above the critical dimension
    • M. Holmes. Convergence of lattice trees to super-Brownian motion above the critical dimension. Electr. J. Probab., 13:671-755, (2008).
    • (2008) Electr. J. Probab. , vol.13 , pp. 671-755
    • Holmes, M.1
  • 13
    • 0038067433 scopus 로고    scopus 로고
    • The Statistical Mechanics of Interacting Walks
    • Oxford University Press, Oxford
    • E. J. Janse van Rensburg. The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles. Oxford University Press, Oxford, (2000).
    • (2000) Polygons, Animals and Vesicles
    • Janse Van Rensburg, E.J.1
  • 14
    • 0000272507 scopus 로고
    • Cell growth problems
    • D.A. Klarner. Cell growth problems. Canad. J. Math., 19:851-863, (1967).
    • (1967) Canad. J. Math. , vol.19 , pp. 851-863
    • Klarner, D.A.1
  • 15
    • 0000240574 scopus 로고
    • Rigorous results for branched polymer models with excluded volume
    • D.J. Klein. Rigorous results for branched polymer models with excluded volume. J. Chem. Phys., 75:5186-5189, (1981).
    • (1981) J. Chem. Phys. , vol.75 , pp. 5186-5189
    • Klein, D.J.1
  • 16
    • 21844486840 scopus 로고
    • 1/d-expansions for the free energy of lattice animal models of a self-interacting branched polymer
    • PJ. Peard and D.S. Gaunt. 1/d-expansions for the free energy of lattice animal models of a self-interacting branched polymer. J. Phys. A: Math. Gen., 28:6109-6124, (1995).
    • (1995) J. Phys. A: Math. Gen. , vol.28 , pp. 6109-6124
    • Peard, P.J.1    Gaunt, D.S.2
  • 17
    • 0000705654 scopus 로고
    • On the spread-out limit for bond and continuum percolation
    • M.D. Penrose. On the spread-out limit for bond and continuum percolation. Ann. Appl. Probab., 3:253-276, (1993).
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 253-276
    • Penrose, M.D.1
  • 18
    • 21844489840 scopus 로고
    • Self-avoiding walks and trees in spread-out lattices
    • M.D. Penrose. Self-avoiding walks and trees in spread-out lattices. J. Stat. Phys., 77:3-15, (1994).
    • (1994) J. Stat. Phys. , vol.77 , pp. 3-15
    • Penrose, M.D.1
  • 19
    • 34247143845 scopus 로고    scopus 로고
    • Springer, Berlin, Lecture Notes in Mathematics Vol, Ecole d’Eté de Probabilités de Saint-Flour XXXIV-2004
    • G. Slade. The Lace Expansion and its Applications. Springer, Berlin, (2006). Lecture Notes in Mathematics Vol. 1879. Ecole d’Eté de Probabilités de Saint-Flour XXXIV-2004.
    • (2006) The Lace Expansion and Its Applications , vol.1879
    • Slade, G.1
  • 20
    • 0003652674 scopus 로고    scopus 로고
    • volume, Cambridge University Press, Cambridge
    • R.P Stanley. Enumerative Combinatorics, volume 1. Cambridge University Press, Cambridge, (1997).
    • (1997) Enumerative Combinatorics , vol.1
    • Stanley, R.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.