منابع مشابه
Uniformity of the Uncovered Set of Random Walk and Cutoff for Lamplighter Chains
We show that the measure on markings of Zn, d ≥ 3, with elements of {0,1} given by i.i.d. fair coin flips on the range R of a random walk X run until time T and 0 otherwise becomes indistinguishable from the uniform measure on such markings at the threshold T = 1 2 Tcov(Z d n). As a consequence of our methods, we show that the total variation mixing time of the random walk on the lamplighter gr...
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We study the convergence to equilibrium of n−samples of independent Markov chains in discrete and continuous time. They are defined as Markov chains on the n−fold Cartesian product of the initial state space by itself, and they converge to the direct product of n copies of the initial stationary distribution. Sharp estimates for the convergence speed are given in terms of the spectrum of the in...
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A sequence of Markov chains is said to exhibit cutoff if the convergence to stationarity in total variation distance is abrupt. We prove a necessary and sufficient condition for cutoff in reversible lazy chains in terms of concentration of hitting time of certain sets of large stationary measure. (Previous works of Aldous, Oliviera, Sousi and the speaker established a less precise connection be...
متن کاملThe cutoff phenomenon in finite Markov chains.
Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to ...
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For any distribution π on {1, 2, . . . , n}, we study elements drawn at random from the set Aπ of tridiagonal stochastic matrices K satisfying π(i)K[i, j] = π(j)K[j, i] for all i, j ∈ [n]. These matrices correspond to birth and death chains with stationary distribution π. We analyze an algorithm for sampling from Aπ and use results from this analysis to draw conclusions about typical elements o...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2018
ISSN: 1083-6489
DOI: 10.1214/18-ejp196