Let mij be the mean first passage time from state i to state j in an n-state ergodic homogeneous Markov chain with transition matrix T . Let G be the weighted digraph without loops whose vertex set is the set of states of the Markov chain and arc weights are equal to the corresponding transition probabilities. We show that

Given an abelian group G endowed with a T=R/Z-pre-symplectic form, we assign to it symplectic twisted ?-algebra WG and then provide criteria for the uniqueness of states invariant under ergodic action automorphism. As application, discuss notion natural in quantum Chern-Simons theory.

Hermon and Hutchcroft have recently proved the long-standing conjecture that in Bernoulli(p) bond percolation on any nonamenable transitive graph G, at p>pc(G), probability cluster of origin is finite but has a large volume n decays exponentially n. A corollary all infinite clusters anchored expansion almost surely. They asked if these results could hold more generally, for energy ergodic invar...

Let C be a bounded closed convex subset of a uniformly convex Banach space X and let = = {T (t) : t ∈ G} be a commutative semigroup of asymptotically nonexpansive in the intermediate mapping from C into itself. In this paper, we provide the strong mean ergodic convergence theorem for the almost-orbit of =.

We prove a max-min theorem for weak containment in the context of algebraic actions. Namely, we show that given an action $G$ on $X,$ there is maximal, closed $G$-invariant subgroup $Y$ $X$ so weakly contained Bernoulli shift. This also minimal any shift $G\curvearrowright X/Y$-ergodic presence X$. give several applications, including major simplification proof measure entropy equals topologica...

We present a class of integer sequences fc n g with the property that for every p-invariant and ergodic positive-entropy measure on T, fc n x (mod 1)g is uniformly distributed for-almost every x. This extends a result of B. Host, who proved this for the sequence fq n g, for q relatively prime to p. Our class of sequences includes, for instance, the sequence c n = P f i (n)q n i , where the numb...

We study invariant random subgroups (IRSs) of semidirect products G = AoΓ. In particular, we characterize all IRSs of parabolic subgroups of SLd(R), and show that all ergodic IRSs of Rdo SLd(R) are either of the form RdoK for some IRS of SLd(R), or are induced from IRSs of Λo SL(Λ), where Λ < Rd is a lattice.

We recall that a probability measure ν on X is said to be μ-stationary if one has μ ∗ ν = ν. It is then said to be μ-ergodic if it is extremal among μ-stationary probability measures. We will say that a probability measure ν on X is homogeneous if it is supported by a closed orbit F of its stabilizer Gν := {g ∈ G | g∗ν = ν}. Such a probability is a finite average of probability measures which a...

A translation surface on (S,Σ) gives rise to two transverse measured foliations F ,G on S with singularities in Σ, and by integration, to a pair of cohomology classes [F ], [G] ∈ H(S,Σ;R). Given a measured foliation F , we characterize the set of cohomology classes b for which there is a measured foliation G as above with b = [G]. This extends previous results of Thurston [Th] and Sullivan [Su]...

In this work, we present a unified performance analysis of a free-space optical (FSO) link that accounts for pointing errors and both types of detection techniques (i.e. intensity modulation/direct detection as well as heterodyne detection). More specifically, we present unified exact closed-form expressions for the cumulative distribution function, the probability density function, the moment ...