arXiv subjects
Publications and source records attributed to L. Saloff-Coste.
We study time-inhomogeneous Markov chains with finite state spaces using Nash and logarithmic-Sobolev inequalities, and the notion of $c$-stability. We develop the basic theory of such functional inequalities in the time-inhomogeneous context and provide illustrating examples.
Starting from a given Markov kernel on a finite set $V$ and a bijection $g$ of $V$, we construct and study a time inhomogeneous Markov chain whose kernel at time $n$ is obtained from $K$ by transport of $g^{n-1}$. We show that this construction leads to interesting examples, and we obtain quantitative results for some of these examples.
We give refined estimates for the discrete time and continuous time versions of some basic random walks on the symmetric and alternating groups $S_n$ and $A_n$. We consider the following models: random transposition, transpose top with random, random insertion, and walks generated by the uniform measure on a conjugacy class. In the case of random walks on $S_n$ and $A_n$ generated by the uniform measure on a conjugacy class, we show that in continuous time the $\ell^2$-cuttoff has a lower bound of $(n/2)\log n$. This result, along with the results of Müller, Schlage-Puchta and Roichman, demonstrates that the continuous time version of these walks may take much longer to reach stationarity than its discrete time counterpart.
For a locally compact group, property RD gives a control on the convolution norm of any compactly supported measure in terms of the $L^2$-norm of its density and the diameter of its support. We give a complete classification of those Lie groups with property RD.