Functional CLT for random walk among bounded random conductances.
Functional inequalities and uniqueness of the Gibbs measure — from log-Sobolev to Poincaré
In a statistical mechanics model with unbounded spins, we prove uniqueness of the Gibbs measure under various assumptions on finite volume functional inequalities. We follow Royer's approach (Royer, 1999) and obtain uniqueness by showing convergence properties of a Glauber-Langevin dynamics. The result was known when the measures on the box [-n,n]d (with free boundary conditions) satisfied the same logarithmic Sobolev inequality. We generalize this in two directions: either the constants may be...
Functional inequalities for discrete gradients and application to the geometric distribution
We present several functional inequalities for finite difference gradients, such as a Cheeger inequality, Poincaré and (modified) logarithmic Sobolev inequalities, associated deviation estimates, and an exponential integrability property. In the particular case of the geometric distribution on we use an integration by parts formula to compute the optimal isoperimetric and Poincaré constants, and to obtain an improvement of our general logarithmic Sobolev inequality. By a...
Functional inequalities for discrete gradients and application to the geometric distribution
We present several functional inequalities for finite difference gradients, such as a Cheeger inequality, Poincaré and (modified) logarithmic Sobolev inequalities, associated deviation estimates, and an exponential integrability property. In the particular case of the geometric distribution on we use an integration by parts formula to compute the optimal isoperimetric and Poincaré constants, and to obtain an improvement of our general logarithmic Sobolev inequality. By a limiting procedure we...
Functional integral representations for self-avoiding walk.
Gaussian estimates for symmetric simple exclusion processes
Gaussian scaling for the critical spread-out contact process above the upper critical dimension.
Gaussian solutions to the lagrangian variational problem in stochastic mechanics
General approximation method for the distribution of Markov processes conditioned not to be killed
We consider a strong Markov process with killing and prove an approximation method for the distribution of the process conditioned not to be killed when it is observed. The method is based on a Fleming−Viot type particle system with rebirths, whose particles evolve as independent copies of the original strong Markov process and jump onto each others instead of being killed. Our only assumption is that the number of rebirths of the Fleming−Viot type system doesn’t explode in finite time almost surely...
General Purpose Model of Queue Dissipation Time at Service Facility with Intermittent Bulk Service Schedule
Generalization of the Modified Bessel Function and Its Generating Function
2000 Mathematics Subject Classification: 33C10, 33-02, 60K25This paper presents new generalizations of the modified Bessel function and its generating function. This function has important application in the transient solution of a queueing system.
Generalization of waiting times model
Generalized canonical states
Generalized harmonic oscillators in quantum probability
Générateurs infinitésimaux des processus à accroissements semi-markoviens
Geodesics and recurrence of random walks in disordered systems.
Geometry of Lipschitz percolation
We prove several facts concerning Lipschitz percolation, including the following. The critical probability pL for the existence of an open Lipschitz surface in site percolation on ℤd with d ≥ 2 satisfies the improved bound pL ≤ 1 − 1/[8(d − 1)]. Whenever p > pL, the height of the lowest Lipschitz surface above the origin has an exponentially decaying tail. For p sufficiently close to 1, the connected regions of ℤd−1 above which the surface has height 2 or more exhibit stretched-exponential...
systems with resident server and generally distributed arrival and service groups.
Giant component and vacant set for random walk on a discrete torus
We consider random walk on a discrete torus of side-length , in sufficiently high dimension . We investigate the percolative properties of the vacant set corresponding to the collection of sites which have not been visited by the walk up to time . We show that when is chosen small, as tends to infinity, there is with overwhelming probability a unique connected component in the vacant set which contains segments of length const . Moreover, this connected component occupies a non-degenerate...
Gibbs–non-Gibbs properties for evolving Ising models on trees
In this paper we study homogeneous Gibbs measures on a Cayley tree, subjected to an infinite-temperature Glauber evolution, and consider their (non-)Gibbsian properties. We show that the intermediate Gibbs state (which in zero field is the free-boundary-condition Gibbs state) behaves differently from the plus and the minus state. E.g. at large times, all configurations are bad for the intermediate state, whereas the plus configuration never is bad for the plus state. Moreover, we show that for each...