Hitting times for random walks on vertex-transitive graphs
نویسندگان
چکیده
منابع مشابه
Hitting times for random walks on vertex-transitive graphs
For random walks on finite graphs, we record some equalities, inequalities and limit theorems (as the size of graph tends to infinity) which hold for vertex-transitive graphs but not for general regular graphs. The main result is a sharp condition for asymptotic exponentiality of the hitting time to a single vertex. Another result is a lower bound for the coefficient of variation of hitting tim...
متن کاملHitting Times for Random Walks with Restarts
The time it takes a random walker in a lattice to reach the origin from another vertex x, has infinite mean. If the walker can restart the walk at x at will, then the minimum expected hitting time γ(x, 0) (minimized over restarting strategies) is finite; it was called the “grade” of x by Dumitriu, Tetali and Winkler. They showed that, in a more general setting, the grade (a variant of the “Gitt...
متن کاملLectures 16-17: Random Walks on Graphs 1.1 Hitting times and Cover Times
Let G (V, E) be an undirected graph. The random walk on G is a Markov chain on V that, at each time step, moves to a uniformly random neighbor of the current vertex. Ffsor x ∈ V , use dx to denote the degree of vertex x. Then more formally, random walk on G is the following process {Xt}. We start at at some node X0 v0 ∈ V . Then if Xt v, we put Xt+1 w with probability 1/dv for every neighbor w ...
متن کاملA Spanning Tree Method for Bounding Hitting Times of Random Walks on Graphs
In this paper we consider the problem of computing the expected hitting time to a vertex for random walks on graphs. We give a method for computing an upper bound on the expected hitting time from an arbitrary spanning tree of the graph. We illustrate this method with two examples. In these examples, we show that the bounds obtained from the spanning method are sharper than bounds obtained from...
متن کاملOn the number of closed walks in vertex-transitive graphs
The results of J. Širáň and the first author (Australasian J. Combin. 10 (1994)) are generalized, and new formulas for the number of closed walks of length p or pq, where p and q are primes, valid for all vertex-transitive graphs are found. Based on these formulas, several simple tests for vertex-transitivity are presented, as well as lower bounds on the orders of the smallest vertexand arc-tra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 1989
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004100068079