Computations of spectral radii on G - spaces Laurent Saloff - Coste and Wolfgang Woess

A Note on the Norms of Transition Operators on Lamplighter Graphs and Groups

Let L X be a lamplighter graph, i.e., the graph-analogue of a wreath product of groups, and let P be the transition operator (matrix) of a random walk on that structure. We explain how methods developed by Saloff-Coste and the author can be applied for determining the p-norms and spectral radii of P , if one has an amenable (not necessarily discrete or unimodular) locally compact group of isome...

Computations of spectral radii on G-spaces

In a series of papers [12], [13], [14] based on ideas introduced by Soardi andWoess [17] and Salvatori [15], we have developed tools to compute the norms and/or spectral radii of Markov operators that are invariant under the left action of a group when the action is either transitive or almost transitive (i.e has a compact factor space). In [12], [13], we where concerned with countable homogene...

Project 01: Random walk models on graphs and groups

Research interests of W. Woess The central topic of the research of W. Woess is “Random Walks on Infinite Graphs and Groups”, which is also the title of the quite successful monograph [7]. Here, Random Walks are understood as Markov chains whose transition probabilities are adapted to an algebraic, geometric, resp. combinatorial structure of the underlying state space. The main theme is the int...

Sobolev Inequalities in Familiar and Unfamiliar Settings

The classical Sobolev inequalities play a key role in analysis in Euclidean spaces and in the study of solutions of partial differential equations. In fact, they are extremely flexible tools and are useful in many different settings. This paper gives a glimpse of assortments of such applications in a variety of contexts.

Lectures on finite Markov chains