Tight Markov chains and random compositions
نویسندگان
چکیده
منابع مشابه
Random walks and Markov chains
This lecture discusses Markov chains, which capture and formalize the idea of a memoryless random walk on a finite number of states, and which have wide applicability as a statistical model of many phenomena. Markov chains are postulated to have a set of possible states, and to transition randomly from one state to a next state, where the probability of transitioning to a particular next state ...
متن کاملMarkov Chains and Random Walks
Let G = (V,E) be a connected, undirected graph with n vertices and m edges. For a vertex v ∈ V , Γ(v) denotes the set of neighbors of v in G. A random walk on G is the following process, which occurs in a sequence of discrete steps: starting at a vertex v0, we proceed at the first step to a random edge incident on v0 and walking along it to a vertex v1, and so on. ”Random chosen neighbor” will ...
متن کاملLecture 7: Markov Chains and Random Walks
A transition probability Pij corresponds to the probability that the state at time step t+1 will be j, given that the state at time t is i. Therefore, each row in the matrix M is a distribution and ∀i, j ∈ SPij ≥ 0 and ∑ j Pij = 1. Let the initial distribution be given by the row vector x ∈ R, xi ≥ 0 and ∑ i xi = 1. After one step, the new distribution is xM. It is easy to see that xM is again ...
متن کاملCoupling methods for random topological Markov chains
We apply coupling techniques in order to prove that the transfer operators associated with random topological Markov chains and non-stationary shift spaces with the big images and preimages property have a spectral gap.
متن کاملTight Inequalities among Set Hitting times in Markov Chains
Given an irreducible discrete-time Markov chain on a finite state space, we consider the largest expected hitting time T (α) of a set of stationary measure at least α for α ∈ (0, 1). We obtain tight inequalities among the values of T (α) for different choices of α. One consequence is that T (α) ≤ T (1/2)/α for all α < 1/2. As a corollary we have that, if the chain is lazy in a certain sense as ...
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: The Annals of Probability
سال: 2012
ISSN: 0091-1798
DOI: 10.1214/11-aop656