3 citations · 3 across the 5 of their papers we have counts for
5 papers
Graphical proof of Ginibre's inequality
Yuki Tokushige
In this short note, we will give a new combinatorial proof of Ginibre's inequality for XY models. Our proof is based on multigraph representations introduced by van Engelenburg-Lis…
Scaling limits for random walks on long range percolation clusters
Noam Berger, Yuki Tokushige
We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two…
Differentiability of the speed of biased random walks on Galton-Watson trees
Adam Bowditch, Yuki Tokushige
We prove that the speed of a -biased random walk on a supercritical Galton-Watson tree is differentiable for such that the walk is ballistic and obeys a central limit theore…
Besov spaces and random walks on a hyperbolic group: boundary traces and reflecting extensions of Dirichlet forms
Pierre Mathieu, Yuki Tokushige
We show the existence of a trace process at infinity for random walks on hyperbolic groups of conformal dimension < 2 and relate it to the existence of a reflecting random walk. To…
Jump processes on the boundaries of random trees
Yuki Tokushige
Kigami showed that a transient random walk on a deterministic infinite tree induces its trace process on the Martin boundary of . In this paper, we will deal with trace proc…