133 research outputs found
Semi-classical analysis of a random walk on a manifold
We prove a sharp rate of convergence to stationarity for a natural random
walk on a compact Riemannian manifold . The proof includes a detailed
study of the spectral theory of the associated operator.Comment: Published in at http://dx.doi.org/10.1214/09-AOP483 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Dispersion for the wave equation outside a ball and counterexamples
The purpose of this note is to prove dispersive estimates for the wave
equation outside a ball in R^d. If d = 3, we show that the linear flow
satisfies the dispersive estimates as in R^3. In higher dimensions d 4 we
show that losses in dispersion do appear and this happens at the Poisson spot
Dispersion for the wave equation inside strictly convex domains I: the Friedlander model case
We consider a model case for a strictly convex domain of dimension
with smooth boundary and we describe dispersion for the wave equation with
Dirichlet boundary conditions. More specifically, we obtain the optimal fixed
time decay rate for the smoothed out Green function: a loss occurs
with respect to the boundary less case, due to repeated occurrences of
swallowtail type singularities in the wave front set.Comment: 53 pages, 4 figures, to appear in Annals of Math. Fixed typos, added
remark
Gibbs/Metropolis algorithms on a convex polytope
This paper gives sharp rates of convergence for natural versions of the
Metropolis algorithm for sampling from the uniform distribution on a convex
polytope. The singular proposal distribution, based on a walk moving locally in
one of a fixed, finite set of directions, needs some new tools. We get useful
bounds on the spectrum and eigenfunctions using Nash and Weyl-type
inequalities. The top eigenvalues of the Markov chain are closely related to
the Neuman eigenvalues of the polytope for a novel Laplacian.Comment: 21 pages, 1 figur
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