arXiv subjects

O. Zeitouni

Publications and source records attributed to O. Zeitouni.

3 recordsLinked to original sources

arXiv2014

Quenched large deviations for one dimensional nonlinear filtering

Consider the standard, one dimensional, nonlinear filtering problem for a diffusion processe $Ξ_t$ observed in small additive white noise. Denote by $q^ε_1(\cdot)$ the density of the law of $Ξ_1$ conditioned on $σ(Y_t^ε: 0\leq t\leq 1)$. We provide "quenched" large deviation estimates for the random family of measures $q^ε_1(x)dx$: there exists a continuous, explicit mapping $\bar J : R^2\to R$ such that for almost all $B_\cdot,V_\cdot$, $\bar J(\cdot,X_1)$ is a good rate function and for any measurable $G\subset R$, $$-\inf_{x\in G^o} \bar J(x,X_1) \leq \liminf ε\log \int_G q_1^ε(x) dx \leq \limsup ε\log \int_G q_1^ε(x) dx \leq -\inf_{x\in \bar G} \bar J(x,X_1) .$$

math.PR↗

arXiv2009

Large deviations of empirical zero point measures on Riemann surfaces, I: $g = 0$

We prove an LDP for the empirical measure of complex zeros of a Gaussian random complex polynomial of degree N of one variable as N tends to infinity. The Gaussian measure is induced by an inner product defined by a smooth weight (Hermitian metric) $h$ and a Bernstein-Markov measure $ν$. The speed is N^2 and the the unique minimizer of the rate function $I$ is the weighted equilibrium measure $ν_{h, K}$ with respect to $h$ on the support $K$ of $ν$.

math.PR↗

arXiv1998

On increasing subsequences of iid samples

We study the fluctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation.

math.PR↗