منابع مشابه
Bounding Fastest Mixing
In a series of recent works, Boyd, Diaconis, and their co-authors have introduced a semidefinite programming approach for computing the fastest mixing Markov chain on a graph of allowed transitions, given a target stationary distribution. In this paper, we show that standard mixing-time analysis techniques—variational characterizations, conductance, canonical paths—can be used to give simple, n...
متن کاملFastest Mixing Markov Chain on a Path
Simulation using Markov chain Monte Carlo is a mainstay of scientific computing; see, e.g., [4, 5] for pointers to the literature. Thus the analysis and design of fast mixing Markov chains, with given stationary distribution, has become a research area. In [2], we show how to numerically find the fastest mixing Markov chain (i.e., the one with smallest secondlargest eigenvalue modulus) on a giv...
متن کاملComparison Inequalities and Fastest-mixing Markov Chains
We introduce a new partial order on the class of stochastically monotone Markov kernels having a given stationary distribution π on a given finite partially ordered state space X . When K L in this partial order we say that K and L satisfy a comparison inequality. We establish that if K1, . . . ,Kt and L1, . . . , Lt are reversible and Ks Ls for s = 1, . . . , t, then K1 · · ·Kt L1 · · ·Lt. In ...
متن کاملFastest Mixing Markov Chain on a Graph
We consider a symmetric random walk on a connected graph, where each edge is labeled with the probability of transition between the two adjacent vertices. The associated Markov chain has a uniform equilibrium distribution; the rate of convergence to this distribution, i.e., the mixing rate of the Markov chain, is determined by the second largest (in magnitude) eigenvalue of the transition matri...
متن کاملBounding the mixing time via coupling
It is convenient to transform G to a directed graph ←→ G , and look at absorbences of G. From G, we form ←→ G by replacing each edge (u, v) by a pair of anti-parallel edges −→ uv and −→ vu. An absorbence rooted at a vertex r of a directed graph is a subset S of edges, such that |S| = |V | − 1 and every vertex, except r, has exactly one edge directed away from it, thus S forms a tree rooted at r...
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: Electronic Communications in Probability
سال: 2005
ISSN: 1083-589X
DOI: 10.1214/ecp.v10-1169