On subadditive processes on direct product of countable amenable groups

on direct sums of baer modules

the notion of baer modules was defined recently

Reversibility and potentiality of exclusion processes on countable discrete groups

Transition invariant exclusion processes on discrete groups is discussed in this article, as examples of spatially extended systems. We show that it is reversible if and only if its entropy production vanishes, or iff its speed functions field has some bounded potential, which is expressed in terms of physical states rather than mathematical states in probability space. Moreover, we conclude th...

Ergodic Theorems on Amenable Groups

Ergodic Theorems on Amenable Groups

In 1931, Birkhoff gave a general and rigorous description of the ergodic hypothesis from statistical meachanics. This concept can be generalized by group actions of a large class of amenable groups on σ-finite measure spaces. The expansion of this theory culminated in Lindenstrauss’ celebrated proof of the general pointwise ergodic theorem in 2001. The talk is devoted to the introduction of abs...

On Connectedness of Graphs on Direct Product of Weyl Groups

In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product o...