scholarly journals Scaling Limits of Loop-Erased Random Walks and Uniform Spanning Trees

2011 ◽  
pp. 791-858 ◽  
Author(s):  
Oded Schramm
Keyword(s):  
Random Walks ◽  
Spanning Trees ◽  
Scaling Limits

scholarly journals Scaling limits for minimal and random spanning trees in two dimensions

1999 ◽  
Vol 15 (3-4) ◽  
pp. 319-367 ◽  
Author(s):  
Michael Aizenman ◽  
Almut Burchard ◽  
Charles M. Newman ◽  
David B. Wilson
Keyword(s):  
Spanning Trees ◽  
Two Dimensions ◽  
Scaling Limits

scholarly journals Conformal invariance of planar loop-erased random walks and uniform spanning trees

2004 ◽  
Vol 32 (1B) ◽  
pp. 939-995 ◽  
Author(s):  
Wendelin Werner ◽  
Oded Schramm ◽  
Gregory F. Lawler
Keyword(s):  
Random Walks ◽  
Conformal Invariance ◽  
Spanning Trees

Correlated continuous-time random walks—scaling limits and Langevin picture

2012 ◽  
Vol 2012 (04) ◽  
pp. P04010 ◽  
Author(s):  
Marcin Magdziarz ◽  
Ralf Metzler ◽  
Wladyslaw Szczotka ◽  
Piotr Zebrowski
Keyword(s):  
Random Walks ◽  
Continuous Time ◽  
Scaling Limits ◽  
Continuous Time Random Walks

Concentration under scaling limits for weakly pinned Gaussian random walks

2008 ◽  
Vol 143 (3-4) ◽  
pp. 441-480 ◽  
Author(s):  
Erwin Bolthausen ◽  
Tadahisa Funaki ◽  
Tatsushi Otobe
Keyword(s):  
Random Walks ◽  
Scaling Limits

On the range of the transient frog model on ℤ

2017 ◽  
Vol 49 (2) ◽  
pp. 327-343 ◽  
Author(s):  
Arka Ghosh ◽  
Steven Noren ◽  
Alexander Roitershtein
Keyword(s):  
Random Walk ◽  
Lower Bound ◽  
Random Walks ◽  
Explicit Formula ◽  
Infinite System ◽  
Scaling Limits ◽  
Interacting Random Walks ◽  
Degenerate Distribution ◽  
Frog Model ◽  
Asymptotic Scaling

Abstract We observe the frog model, an infinite system of interacting random walks, on ℤ with an asymmetric underlying random walk. For certain initial frog distributions we construct an explicit formula for the moments of the leftmost visited site, as well as their asymptotic scaling limits as the drift of the underlying random walk vanishes. We also provide conditions in which the lower bound can be scaled to converge in probability to the degenerate distribution at 1 as the drift vanishes.

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