439 research outputs found
Merging for inhomogeneous finite Markov chains, part II: Nash and log-Sobolev inequalities
We study time-inhomogeneous Markov chains with finite state spaces using Nash
and logarithmic-Sobolev inequalities, and the notion of -stability. We
develop the basic theory of such functional inequalities in the
time-inhomogeneous context and provide illustrating examples.Comment: Published in at http://dx.doi.org/10.1214/10-AOP572 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Time inhomogeneous Markov chains with wave-like behavior
Starting from a given Markov kernel on a finite set and a bijection
of , we construct and study a time inhomogeneous Markov chain whose kernel
at time is obtained from by transport of . We show that this
construction leads to interesting examples, and we obtain quantitative results
for some of these examples.Comment: Published in at http://dx.doi.org/10.1214/09-AAP661 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Random walks on free solvable groups
For any finitely generated group G, let n ---> \Phi_G(n) be the function that
describes the rough asymptotic behavior of the probability of return to the
identity element at time 2n of a symmetric simple random walk on G (this is an
invariant of quasi-isometry). We determine this function when G is the free
solvable group S_{d,r} of derived length d on r generators and some other
related groups
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