The Construction, and Other General Results.- Some Basic Tools.- Spin Systems.- Stochastic Ising Models.- The Voter Model.- The Contact Process.- Nearest-Particle Systems.- The Exclusion Process.-… Expand

A new approach of financial volatility duration dynamics by stochastic interacting systems contact voter and core and passage time moments and hybrid zones for the exclusion.Expand

Abstract : The authors continue a discussion of a problem posed by Hille (1951) in a paper titled, 'On the Generation of Semigroups and the Theory of Conjugate Functions.'

We consider families of(0,1)-valued random variables indexed by the vertices of countable graphs with bounded degree. First we show that if these random variables satisfy the property that… Expand

SummaryLet W1,..., WN be N nonnegative random variables and let
$$\mathfrak{M}$$
be the class of all probability measures on [0, ∞). Define a transformation T on
$$\mathfrak{M}$$
by letting Tμ be… Expand

We introduce the class of strongly Rayleigh probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter. This class covers… Expand

Consider the infinite particle system on the countable set $S$ with the simple exclusion interaction and one-particle motion determined by the stochastic transition matrix $p(x, y)$. In the past, the… Expand

Aldous' spectral gap conjecture asserts that on any graph the random walk process and the random transposition (or interchange) process have the same spectral gap. We prove the conjecture using a… Expand