The Mixing Time of Glauber Dynamics for Colouring Regular Trees
نویسندگان
چکیده
We consider Metropolis Glauber dynamics for sampling proper qcolourings of the n-vertex complete b-ary tree when 3 ≤ q ≤ b/2 ln(b). We give both upper and lower bounds on the mixing time. For fixed q and b, our upper bound is nO(b/ log b) and our lower bound is nΩ(b/q log(b)), where the constants implicit in the O() and Ω() notation do not depend upon n, q or b.
منابع مشابه
Matrix norms and rapid mixing for spin systems
We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the associated dependency matrix is less than 1. We give improved analysis for the case in which the diagonal of the dependency matrix is 0 (as in heat bath dynamics...
متن کاملGlauber Dynamics for Sampling an Edge Colouring of Regular Trees
We study the problem of sampling a graph colouring using Glauber Dynamics. This is an interesting problem as Jerrum showed that we can approximate the number of proper colouring if we can sample a colouring nearly uniformly. Therefore we want a sampler with polynomial running time. Glauber Dynamics is one natural Markov Chain for sampling a graph colouring and it has been studied extensively. T...
متن کاملGlauber dynamics on trees: Boundary conditions and mixing time†
We give the first comprehensive analysis of the effect of boundary conditions on the mixing time of the Glauber dynamics in the so-called Bethe approximation. Specifically, we show that spectral gap and the log-Sobolev constant of the Glauber dynamics for the Ising model on an n-vertex regular tree with (+)-boundary are bounded below by a constant independent of n at all temperatures and all ex...
متن کامل2 5 Ju l 2 00 3 Glauber dynamics on trees : Boundary conditions and mixing time †
We give the first comprehensive analysis of the effect of boundary conditions on the mixing time of the Glauber dynamics in the so-called Bethe approximation. Specifically, we show that spectral gap and the log-Sobolev constant of the Glauber dynamics for the Ising model on an n-vertex regular tree with (+)-boundary are bounded below by a constant independent of n at all temperatures and all ex...
متن کاملThe Ising Model on Trees: Boundary Conditions and Mixing Time
We give the first comprehensive analysis of the effect of boundary conditions on the mixing time of the Glauber dynamics for the Ising model. Specifically, we show that the mixing time on an -vertex regular tree with -boundary remains at all temperatures (in contrast to the free boundary case, where the mixing time is not bounded by any fixed polynomial at low temperatures). We also show that t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Random Struct. Algorithms
دوره 36 شماره
صفحات -
تاریخ انتشار 2010