Some properties of the numbers of lattice animals and lattice trees

1990 ◽  
Vol 5 (3) ◽  
pp. 307-308 ◽  
Author(s):  
Christine E. Soteros ◽  
Stuart G. Whittington
Keyword(s):  
Lattice Animals ◽  
Lattice Trees

On the upper critical dimension of lattice trees and lattice animals

1990 ◽  
Vol 59 (5-6) ◽  
pp. 1469-1510 ◽  
Author(s):  
Takashi Hara ◽  
Gordon Slade
Keyword(s):  
Critical Dimension ◽  
Lattice Animals ◽  
Upper Critical Dimension ◽  
Lattice Trees

scholarly journals Collapsing lattice animals and lattice trees in two dimensions

2005 ◽  
Vol 2005 (06) ◽  
pp. P06003 ◽  
Author(s):  
Hsiao-Ping Hsu ◽  
Peter Grassberger
Keyword(s):  
Two Dimensions ◽  
Lattice Animals ◽  
Lattice Trees

scholarly journals Correction to: NoBLE for Lattice Trees and Lattice Animals

2022 ◽  
Vol 186 (2) ◽  
Author(s):  
Robert Fitzner ◽  
Remco van der Hofstad
Keyword(s):  
Lattice Animals ◽  
Lattice Trees

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

2011 ◽  
Vol 16 (0) ◽  
pp. 129-136 ◽  
Author(s):  
Yuri Mejia Miranda ◽  
Gordon Slade
Keyword(s):  
Lattice Animals ◽  
High Dimensions ◽  
Lattice Trees ◽  
Growth Constants

scholarly journals Expansion in High Dimension for the Growth Constants of Lattice Trees and Lattice Animals

2013 ◽  
Vol 22 (4) ◽  
pp. 527-565 ◽  
Author(s):  
YURI MEJÍA MIRANDA ◽  
GORDON SLADE
Keyword(s):  
Error Estimates ◽  
High Dimension ◽  
Integer Lattice ◽  
Nearest Neighbour ◽  
Lattice Animals ◽  
Lace Expansion ◽  
Lattice Trees ◽  
Growth Constants ◽  
The One ◽  
Rigorous Error

We compute the first three terms of the 1/d expansions for the growth constants and one-point functions of nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice $\mathbb{Z}^d$, with rigorous error estimates. The proof uses the lace expansion, together with a new expansion for the one-point functions based on inclusion–exclusion.

General model for collapse in lattice animals

1992 ◽  
Vol 25 (19) ◽  
pp. L1169-L1172 ◽  
Author(s):  
S Flesia ◽  
D S Gaunt ◽  
C E Soteros ◽  
S G Whittington
Keyword(s):  
General Model ◽  
Lattice Animals

scholarly journals Crossing Velocities and Random Lattice Animals

1995 ◽  
Vol 23 (3) ◽  
pp. 1006-1023 ◽  
Author(s):  
Alain-Sol Sznitman
Keyword(s):  
Lattice Animals ◽  
Random Lattice
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