We consider a continuous gas in d-dimensional rectangular box with finite range, positive pair potential, and we construct Markov process which particles appear disappear appropriate rates so that the is reversible w.r.t. Gibbs measure. If thermodynamical paramenters are such specification satisfies certain mixing condition, then spectral gap of generator strictly uniformly volume boundary condition. The required condition holds if, for instance, there convergent cluster expansion. Dans une...

We consider a conservative stochastic spin exchange dynamics which is reversible with respect to the canonical Gibbs measure of lattice gas model. assume that corresponding grand satisfies suitable strong mixing condition. give an alternative and quite natural, from physical point view, proof famous Lu–Yau result states relaxation time in box side L scales like L2. then show how use such estimate prove decay equilibrium for local functions form 1/tα−ε, where ε positive arbitrarily small α=12...

We have investigated the presence of a phase separation in diagram Kondo-like spin-hole coupled model. Within mean-field analysis we find that system normal separates into spin liquid and Fermi phase. The introduction superconducting order parameter stabilizes strongly reducing region. A reasonable behaviour Tc vs. doping δ is also obtained.

We study, in two space dimensions, the heat equation with a random potential that is white noise and time. introduce regularization of prove that, by suitable renormalization coupling coefficient, covariance has non-trivial limit when removed. The described terms two-body Schrödinger operator singular interaction.

We analyze the density and size dependence of relaxation time $\tau$ for kinetically constrained spin systems. These have been proposed as models strong or fragile glasses systems undergoing jamming transitions. For one (FA1f) two (FA2f) facilitated Fredrickson-Andersen model at any $\rho<1$ Knight below critical which glass transition occurs, we show that persistence spin-spin auto-correlation functions decay exponentially. This excludes stretched exponential was derived by numerical...

Abstract We consider a conservative stochastic spin exchange dynamics reversible with respect to the canonical Gibbs measure of lattice gas model. assume that corresponding grand satisfies suitable strong mixing condition. Following previous work by two us for spectral gap, we provide an alternative and quite natural, from physical point view, proof well known result Yau stating logarithmic Sobolev constant in box side L grows like  2 .

We consider the Fredrickson and Andersen one spin facilitated model (FA1f) on an infinite connected graph with polynomial growth. Each site rate refreshes its occupation variable to a filled or empty state probability $p\in[0,1]$ $q=1-p$ respectively, provided that at least of nearest neighbours is empty. study non-equilibrium dynamics started from initial distribution $ν$ different stationary product $p$-Bernoulli measure $μ$. assume that, under $ν$, mean distance between two sites...

If $P_t$ is the semigroup associated with Kawasaki dynamics on $Z^d$ and $f$ a local function configuration space, then variance respect to invariant measure $\mu$ of $P_t f$ goes zero as $t\to \infty$ faster than $t^{-d/2+\varepsilon}$, $\varepsilon$ arbitrarily small. The fundamental assumption mixing condition interaction Dobrushin Schlosman type.

We prove tight bounds on the relaxation time of so-called L-reversal chain, which was introduced by R. Durrett as a stochastic model for evolution chromosome chains. The process is described follows. have n distinct letters vertices n-cycle (ℤ mod n); at each step, connected subset graph chosen uniformly random among all those length most L, and current permutation shuffled reversing order over that subset. show τ(n, L), defined inverse spectral gap associated Markov generator, satisfies...

Consider a finite number of balls initially placed in $L$ bins. At each time step ball is taken from non-empty bin. Then all the are uniformly reassigned into This Markov chain called Repeated Balls-into-Bins process and discrete interacting particle system with parallel updating. We prove that, starting suitable (chaotic) set initial states, as $L\to+\infty$, numbers bin becomes independent rest i.e. we have propagation chaos. furthermore study some equilibrium properties limiting nonlinear process.

Vegetable oils (VO) can provide sustainable feedstock to substitute chemicals currently obtained from petrol. VO are majorly composed of saturated or unsaturated fatty acids with 18 carbon atoms (C18), free esterifying glycerol. The monounsaturated C18 acid (C18:1, oleic acid) is industrial interest. Heterogeneous catalytic selective hydrogenation studied maximize the fraction C18:1 in VO. current work investigates modelling point view, examining relation between deterministic models (based...

On the rooted $k$-ary tree we consider a 0-1 kinetically constrained spin model in which occupancy variable at each node is re-sampled with rate one from Bernoulli(p) measure iff all its children are empty. For this process following picture was conjectured to hold. As long as $p$ below percolation threshold $p_c=1/k$ ergodic finite relaxation time while, for $p>p_c$, on infinite no longer and regular sub-tree becomes exponentially large depth of tree. At critical point $p=p_c$ still but an...