Markov chainMixing timeMany modern techniques employed in physics, such a computation of path integrals, rely on random walks on graphs that can be represented as Markov chains. Traditionally, estimates of running times of such sampling algorithms are computed using the number of steps in the ...
由此可以引申出mixing time的概念，按照Markov Chains and Mixing Times, second edition的定义：The numbe...
We introduce Markov chains to sample the 1–2 model configurations on the 2D hexagonal lattice and prove that the mixing time of these chains is polynomial in the sizes of the graphs for a large class of probability measures.This is a preview of subscription content, log in via an ...
由此可以引申出mixing time的概念，按照Markov Chains and Mixing Times, second edition的定义：The numbe...
Elements of S can be interpreted as various possible states of whatever system we are interested in studying, and pij represents the probability that the system is in state j at time n+ 1, if it is state i at time n. We will think of a Markov chain as a stochastic process with ...
and Chapter 24 that relates mixing times and hitting time parameters to stationary stopping times. Chapter 4 now includes an introduction to mixing times in lp, which reappear in Chapter 10. The latter chapter has several new topics, including estimates for hitting times on trees and Eulerian dig...
Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Sampling Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for ...
We prove an upper bound of O((n + k) log4 n) for the mixing time of the top-swap Markov chain with n cards and k decks. Previously, the best known upper bound was O((n + k)2 log(n + k)), following from the relaxation time bound proved in [1]. We also obtain a mixing...
For an irreducible stochastic matrix T, the Kemeny constant K(T) measures the expected time to mixing of the Markov chain corresponding to T. Given a strongly connected directed graph D, we consider the set ΣD of stochastic matrices whose directed graph is subordinate to D, and compute the...
We model the dispatching process in rideshare as a Markov chain that takes into account the geographic mobility of both drivers and riders over time. Prior work explores dispatch policies in the limit of such Markov chains; we characterize when this limit assumption is valid, under a variety of...