Point processes, hole events, and large deviations: random complex zeros and Coulomb gases
We consider particle systems (also known as point processes) on the line and in the plane
and are particularly interested in “hole” events, when there are no particles in a large disk (or …
and are particularly interested in “hole” events, when there are no particles in a large disk (or …
The forbidden region for random zeros: appearance of quadrature domains
Our main discovery is a surprising interplay between quadrature domains on the one hand,
and the zeros of the Gaussian Entire Function (GEF) on the other. Specifically, consider the …
and the zeros of the Gaussian Entire Function (GEF) on the other. Specifically, consider the …
Local universality for real roots of random trigonometric polynomials
Consider a random trigonometric polynomial X_n:R→R of the form X_n(t)=∑_k=1^n\left(ξ_k\
sin(kt)+η_k\cos(kt)\right), where (ξ_1,η_1),(ξ_2,η_2),... are independent identically …
sin(kt)+η_k\cos(kt)\right), where (ξ_1,η_1),(ξ_2,η_2),... are independent identically …
Long gaps between sign-changes of Gaussian stationary processes
ND Feldheim, ON Feldheim - … Mathematics Research Notices, 2015 - academic.oup.com
We study the probability of a real-valued stationary process to be positive on a large interval
[0, N]. We show that if in some neighborhood of the origin the spectral measure of the …
[0, N]. We show that if in some neighborhood of the origin the spectral measure of the …
Persistence and Ball exponents for Gaussian stationary processes
Consider a real Gaussian stationary process $ f_\rho $, indexed on either $\mathbb {R} $ or
$\mathbb {Z} $ and admitting a spectral measure $\rho $. We study $\theta_ {\rho}^\ell …
$\mathbb {Z} $ and admitting a spectral measure $\rho $. We study $\theta_ {\rho}^\ell …
Persistence of Gaussian stationary processes: a spectral perspective
N Feldheim, O Feldheim, S Nitzan - 2021 - projecteuclid.org
We study the persistence probability of a centered stationary Gaussian process on Z or R,
that is, its probability to remain positive for a long time. We describe the delicate interplay …
that is, its probability to remain positive for a long time. We describe the delicate interplay …
Effective persistency evaluation via exact excursion distributions for random processes and fields
Finding the probability that a stochastic system stays in a certain region of its state space
over a specified time—a long-standing problem both in computational physics and in …
over a specified time—a long-standing problem both in computational physics and in …
Persistence probabilities in centered, stationary, Gaussian processes in discrete time
M Krishna, M Krishnapur - Indian Journal of Pure and Applied …, 2016 - Springer
Lower bounds for persistence probabilities of stationary Gaussian processes in discrete time
are obtained under various conditions on the spectral measure of the process. Examples are …
are obtained under various conditions on the spectral measure of the process. Examples are …
Persistence of Gaussian stationary processes: a spectral perspective
N Feldheim, O Feldheim, S Nitzan - arXiv preprint arXiv:1709.00204, 2017 - arxiv.org
We study the persistence probability of a centered stationary Gaussian process on $\mathbb
{Z} $ or $\mathbb {R} $, that is, its probability to remain positive for a long time. We describe …
{Z} $ or $\mathbb {R} $, that is, its probability to remain positive for a long time. We describe …
The Slepian model based independent interval approximation of persistency and zero-level exceedance distributions
H Bengtsson, K Podgorski - arXiv preprint arXiv:2401.01805, 2024 - arxiv.org
In physics and engineering literature, the distribution of the excursion-above-zero time
distribution (exceedance distribution) for a stationary Gaussian process has been …
distribution (exceedance distribution) for a stationary Gaussian process has been …