Displaying 241 – 260 of 280

Showing per page

On the volume of intersection of three independent Wiener sausages

M. van den Berg (2010)

Annales de l'I.H.P. Probabilités et statistiques

Let K be a compact, non-polar set in ℝm, m≥3 and let SKi(t)={Bi(s)+y: 0≤s≤t, y∈K} be Wiener sausages associated to independent brownian motions Bi, i=1, 2, 3 starting at 0. The expectation of volume of ⋂i=13SKi(t) with respect to product measure is obtained in terms of the equilibrium measure of K in the limit of large t.

On the zero-temperature or vanishing viscosity limit for certain Markov processes arising from Lagrangian dynamics

Nalini Anantharaman (2004)

Journal of the European Mathematical Society

We study the zero-temperature limit for Gibbs measures associated to Frenkel–Kontorova models on ( d ) / d . We prove that equilibrium states concentrate on configurations of minimal energy, and, in addition, must satisfy a variational principle involving metric entropy and Lyapunov exponents, a bit like in the Ruelle–Pesin inequality. Then we transpose the result to certain continuous-time stationary stochastic processes associated to the viscous Hamilton–Jacobi equation. As the viscosity vanishes, the...

On unique extension of time changed reflecting brownian motions

Zhen-Qing Chen, Masatoshi Fukushima (2009)

Annales de l'I.H.P. Probabilités et statistiques

Let D be an unbounded domain in ℝd with d≥3. We show that if D contains an unbounded uniform domain, then the symmetric reflecting brownian motion (RBM) on ̅D is transient. Next assume that RBM X on ̅D is transient and let Y be its time change by Revuz measure 1D(x)m(x) dx for a strictly positive continuous integrable function m on ̅D. We further show that if there is some r>0 so that D∖̅B̅(̅0̅,̅ ̅r̅) is an unbounded uniform domain, then Y admits one and only one symmetric diffusion that...

One-dimensional finite range random walk in random medium and invariant measure equation

Julien Brémont (2009)

Annales de l'I.H.P. Probabilités et statistiques

We consider a model of random walks on ℤ with finite range in a stationary and ergodic random environment. We first provide a fine analysis of the geometrical properties of the central left and right Lyapunov eigenvectors of the random matrix naturally associated with the random walk, highlighting the mechanism of the model. This allows us to formulate a criterion for the existence of the absolutely continuous invariant measure for the environments seen from the particle. We then deduce a characterization...

Currently displaying 241 – 260 of 280