Diffusive-Ballistic Transition in Random Walks with Long-Range Self-Repulsion
We prove that a class of random walks on $\Z^2$ with long-range self-repulsive interactions have a diffusive-ballistic phase transition.
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arXiv subjects
Remy Sanchis
Publications and source records attributed to Remy Sanchis.
Decay Properties of the Connectivity for Mixed Long Range Percolation Models on $\Z^d$
In this short note we consider mixed short-long range independent bond percolation models on $\Z^{k+d}$. Let $p_{uv}$ be the probability that the edge $(u,v)$ will be open. Allowing a $x,y$-dependent length scale and using a multi-scale analysis due to Aizenman and Newman, we show that the long distance behavior of the connectivity $τ_{xy}$ is governed by the probability $p_{xy}$. The result holds up to the critical point.
math-ph↗