A monotonicity property for random walk in a partially random environment
Mark Holmes,Rongfeng Sun +1 more
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TLDR
In this paper, a law of large numbers for random walks in certain kinds of i.i.d. random environments in Z d was proved, which is an extension of a result of Bolthausen et al. (2003) [4].About:
This article is published in Stochastic Processes and their Applications.The article was published on 2012-04-01 and is currently open access. It has received 14 citations till now. The article focuses on the topics: Random walk & Heterogeneous random walk in one dimension.read more
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Monotonicity for excited random walk in high dimensions
TL;DR: In this article, it was shown that the drift θ(d, β) for excited random walk in dimension d is monotone in the excitement parameter when d ≥ 9.
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Monotonicity for excited random walk in high dimensions
TL;DR: In this paper, it was shown that the drift for excited random walk in dimension $d$ is monotone in the excitement parameter when $d\ge 9$ when d = 0, 1.
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Excited against the tide: A random walk with competing drifts
TL;DR: In this paper, the authors study excited random walks in high dimensions and show that the expected right drift of the first cookie is strictly positive, regardless of the strength and signs of subsequent cookies.
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The continuous-time lace expansion
TL;DR: In this paper, the authors derive a continuous-time lace expansion for a broad class of self-interacting continuous time random walks and apply it to the lattice Edwards model at weak coupling.
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On strict monotonicity of the speed for excited random walks in one dimension
TL;DR: In this article, a direct coupling proof of strict monotonicity of the speed of 1-dimensional multi-excited random walks with positive speed was given, without using branching processes.
References
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Random Walks in Random Environment.
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A law of large numbers for random walks in random environment
TL;DR: In this article, the authors derived a law of large numbers for a class of multidimensional random walks in random environment satisfying a condition which first appeared in the work of Kalikow.
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The lace expansion for self-avoiding walk in five or more dimensions
TL;DR: In this paper, it was proved that the standard model of self-avoiding walk in five or more dimensions has the same critical behaviour as the simple random walk, assuming convergence of the lace expansion.
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Invariance principle for the random conductance model with unbounded conductances.
TL;DR: In this paper, a continuous time random walk X in an environment of i.i.d. random conductances was studied, and heat kernel bounds were obtained and a quenched invariance principle for X was proved.
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Random walks in random environments
TL;DR: In this paper, the authors review the model, available results and techniques, and point out several gaps in the understanding of these processes, and present several gaps that need to be filled.
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A combinatorial result with applications to self-interacting random walks
Mark Holmes,Thomas S. Salisbury +1 more