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14 papers · 2 filters
Local universality of the number of zeros of random trigonometric polynomials with continuous coefficients
Jean-Marc Azaïs, Federico Dalmao, José León +2
Let be a random trigonometric polynomial of degree with iid coefficients and let denote the (random) number of its zeros lying in the compact interval $I\subset\…
Useful bounds on the extreme eigenvalues and vectors of matrices for Harper's operators
Daniel Bump, Persi Diaconis, Angela Hicks +2
In analyzing a simple random walk on the Heisenberg group we encounter the problem of bounding the extreme eigenvalues of an matrix of the form where is a c…
Second order Riesz transforms on multiply-connected Lie groups and processes with jumps
Nicola Arcozzi, Komla Domelevo, Stefanie Petermichl
We study a class of combinations of second order Riesz transforms on Lie groups that are multiply connected, composed of a discrete abelian component and a compact connected compon…
Diffusions with polynomial eigenvectors via finite subgroups of O(3)
Dominique Bakry, Xavier Bressaud
We provide new examples of diffusion operators in dimension 2 and 3 which have orthogonal polynomials as eigenvectors. Their construction rely on the finite subgroups of O(3) and t…
Stochastic regularization effects of semi-martingales on random functions
Romain Duboscq, Anthony Réveillac
In this paper we address an open question formulated in [17]. That is, we extend the It{ô}-Tanaka trick, which links the time-average of a deterministic function f depending on a s…
Estimates on the amplitude of the first Dirichlet eigenvector in discrete frameworks
Persi Diaconis, Laurent Miclo
Consider a finite absorbing Markov generator, irreducible on the non-absorbing states. Perron-Frobenius theory ensures the existence of a corresponding positive eigenvector . Th…