منابع مشابه
Mixing times are hitting times of large sets
We consider irreducible reversible discrete time Markov chains on a finite state space. Mixing times and hitting times are fundamental parameters of the chain. We relate them by showing that the mixing time of the lazy chain is equivalent to the maximum over initial states x and large sets A of the hitting time of A starting from x. We also prove that the first time when averaging over two cons...
متن کاملHitting and commute times in large graphs are often misleading
Next to the shortest path distance, the second most popular distance function between vertices in a graph is the commute distance (resistance distance). For two vertices u and v, the hitting time Huv is the expected time it takes a random walk to travel from u to v. The commute time is its symmetrized version Cuv = Huv + Hvu. In our paper we study the behavior of hitting times and commute dista...
متن کاملMixing and hitting times for finite Markov chains
Let 0 < α < 1/2. We show that that the mixing time of a continuous-time Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of the state space with stationary measure ≥ α. Suitably modified results hold in discrete time and/or without the reversibility assumption. The key technical tool in the proof is the construction of random set A such tha...
متن کاملAsymptotics for Hitting Times
In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class (A) F = F is continuous and concave; F (t) ≤ t for t ≥ 0.. Note that all possible asymptotics are absolutely continuous.
متن کاملRandom walks on dynamical percolation: mixing times, mean squared displacement and hitting times
We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph G are either open or closed and refresh their status at rate μ while at the same time a random walker moves on G at rate 1 but only along edges which are open. On the d-dimensional torus with side length n, we prove that in the subcritical regime, the mixing times for both the full system and the ...
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ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2013
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-013-0497-9