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Indeed, using estimates for the so-called tan points of the simple random walk, introduced in [1] and subse- quently used in [7, 8], it is possible to prove that, when d ≥ 2, the
We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices.. This random walk, already known to be transient, has
Then, to prove IDLA inner bound, we need to show that for each vertex v ∈ V the Green function from 0 and expected exit time from a ball around 0 of a random walk starting at v ,
The authors prove that for large class of random Hamiltonians the point process of properly normalized energies restricted to a sparse enough random subset of spin configuration
In this section we prove the existence of a minimal stopping time which solves the Skorokhod embedding problem for random walk, and make some simple observations which show that
Molloy, Very rapidly mixing Markov chains for 2∆-colourings and for independent sets in a 4-regular graph, Random Struc. Tetali, Mathematical aspects of mixing times in Markov
We prove the moderate deviation principle for subgraph count statistics of Erd˝ os-Rényi random graphs.. This is equivalent in showing the moderate deviation principle for the trace
Thus we have a coupling based proof of the n log n + O ( n ) mixing time bound for the lazy random walk against a Cayley adversary.. This also works against a holomorphic adversary,
