Related papers: Large deviations for the zero set of an analytic f…
On the plane, every random compact set with almost surely uncountable first projection intersects with a high probability the graph of some continuous function. Implication: every black noise over the plane fails to factorize when the plane…
We use asymptotic methods from the theory of differential equations to obtain an analytical expression for the survival probability of an Ornstein-Uhlenbeck process with a potential defined over a broad domain. We form a uniformly…
Our main discovery is a surprising interplay between quadrature domains on the one hand, and the zero process of the Gaussian Entire Function (GEF) on the other. Specifically, consider the GEF conditioned on the rare hole event that there…
We study the probability that a real stationary Gaussian process has at least $\eta T$ zeros in $[0,T]$ (overcrowding), or at most this number (undercrowding). We show that if the spectral measure of the process is supported on $\pm[B,A]$,…
Let $\xi_0,\xi_1,...$ be independent identically distributed (i.i.d.) random variables such that $\E \log (1+|\xi_0|)<\infty$. We consider random analytic functions of the form $$ G_n(z)=\sum_{k=0}^{\infty} \xi_k f_{k,n} z^k, $$ where…
We consider an ensemble of Ornstein-Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable…
Black hole entropy is identified with the counting of the dynamical degrees of freedom of trapped gravitational modes continually sourced by the Hawking-Unruh process. In the context of linear perturbations of Schwarzschild spacetime the…
A classical result due to Blaschke states that for every analytic self-map $f$ of the open unit disk of the complex plane there exists a Blaschke product $B$ such that the zero sets of $f$ and $B$ agree. In this paper we show that there is…
We consider $Z^d$, with d bigger or equal to three. We investigate the vacant set of random interlacements in the strongly percolative regime, the vacant set of the simple random walk, and the excursion set above a given level of the…
We study large deviations, over a long time window $T \to \infty$, of the dynamical observables $A_n = \int_{0}^{T} x^n(t) dt$, $n=3,4,\dots$, where $x(t)$ is a centered stationary Gaussian process in continuous time. We show that, for…
A special type of geometric situation in ensembles of non-intersecting paths occurs when the non-intersecting trajectories are required to be nonnegative so that the limit shape becomes tangential to the hard-edge $0$. The local fluctuation…
Quantization of the gravitational field may allow the existence of a decay channel of black holes into white holes with an explicit time-reversal symmetry. The definition of a meaningful decay probability for this channel is studied in…
We study asymptotic clustering of zeros of random polynomials, and show that the expected discrepancy of roots of a polynomial of degree $n$, with not necessarily independent coefficients, decays like $\sqrt{\log n/n}$. Our proofs rely on…
Combining the mollifiers, we exhibit other choices of coefficients that improve the results on large gaps between the zeros of the Riemann zeta-function. Precisely, assuming the Generalized Riemann Hypothesis (GRH), we show that there exist…
A manifestation of the black hole information loss problem is that the two-point function of probe operators in a large Anti-de Sitter black hole decays in time, whereas, on the boundary CFT, it is expected to be an almost periodic function…
We consider the totally asymmetric exclusion process on a ring in discrete time with the backward-ordered sequential update and particle-dependent hopping probabilities. Using a combinatorial treatment of the Bethe ansatz, we derive the…
Let $X=(X_t)$ be a one-dimensional Ornstein-Uhlenbeck process with an initial density function $f$ supported on the positive real-line that is a regularly varying function with exponent $-(1+\eta)$, with $\eta\in (0,1)$. We prove the…
For hole systems with an effective spin 3/2 we analyzed analytically and numerically the evolution of wave packets with the different initial polarizations. The dynamics of such systems is determined by the $4\times 4$ Luttinger…
The large complex zeros of the Jost function (poles of the S matrix) in the complex wave number-plane for s-wave scattering by truncated potentials are associated to the distribution of large prime numbers as well as to the asymptotic…
We establish a convergence speed estimate for hole probabilities of zeros of random holomorphic sections on compact Riemann surfaces.