Cutoff phenomena for random walks on random regular graphs
نویسندگان
چکیده
منابع مشابه
Cutoff Phenomena for Random Walks on Random Regular Graphs
The cutoff phenomenon describes a sharp transition in the convergence of a family of ergodic finite Markov chains to equilibrium. Many natural families of chains are believed to exhibit cutoff, and yet establishing this fact is often extremely challenging. An important such family of chains is the random walk on G(n, d), a random d-regular graph on n vertices. It is well known that the spectral...
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Reduced `-cohomology in degree 1 (for short "LpR1") is a useful quasiisometry invariant of graphs [of bounded valency] whose definition is relatively simple. On a graph, there is a natural gradient operator from functions to vertices to functions on edges defined by looking at the difference of the value on the extremities of the edge. Simply put, this cohomology is the quotient of functions wi...
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We study properties of multiple random walks on a graph under various assumptions of interaction between the particles. To give precise results, we make the analysis for random regular graphs. The cover time of a random walk on a random r-regular graph was studied in [6], where it was shown with high probability (whp), that for r ≥ 3 the cover time is asymptotic to θrn lnn, where θr = (r − 1)/(...
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For an undirected graph and an optimal cyclic list of all its vertices, the cyclic cover time is the expected time it takes a simple random walk to travel from vertex to vertex along the list, until it completes a full cycle. The main result of this paper is a characterization of the cyclic cover time in terms of simple and easy to compute graph properties. Namely, for any connected graph, the ...
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The cutoff phenomenon for an ergodic Markov chain describes a sharp transition in the convergence to its stationary distribution, over a negligible period of time, known as cutoff window. We study the cutoff phenomenon for simple random walks on Kneser graphs, which is a family of ergodic Markov chains. Given two integers n and k, the Kneser graph K(2n+ k, n) is defined as the graph with vertex...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2010
ISSN: 0012-7094
DOI: 10.1215/00127094-2010-029