Related papers: Universal width distributions in non-Markovian Gau…
The position $x(t)$ of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray $x=v_0 t$, where $v_0$ is the average drift. However,…
We derive a universal asymptotic formula for generic boundary conditions for the average value of the bulk-to-boundary and boundary Operator Product Expansion coefficients of any unitary, compact two-dimensional Boundary CFT (BCFT) with…
We study boundary non-crossing probabilities $$ P_{f,u} := \mathrm P\big(\forall t\in \mathbb T\ X_t + f(t)\le u(t)\big) $$ for continuous centered Gaussian process $X$ indexed by some arbitrary compact separable metric space $\mathbb T$.…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
For fixed $t\in [0,1)$ and $h>0$, consider the local uniform empirical process $$\DD_{n,h,t}(s):=n^{-1/2}\coo\sliin 1_{[t,t+hs]}(U_i)-hs\cff,\;s\in [0,1],$$ where the $U_i$ are independent and uniformly distributed on $[0,1]$. We…
We study a broad class of high-dimensional mean-field exchange models, encompassing both noisy and singular dynamics, along with their dual processes. This includes a generalized version of the averaging process as well as some…
The properties of eigenvalues of large dimensional random matrices have received considerable attention. One important achievement is the existence and identification of the limiting spectral distribution of the empirical spectral…
Under the assumption of the Riemann Hypothesis, the Linear Independence Hypothesis, and a bound on negative discrete moments of the Riemann zeta function, we prove the existence of a limiting logarithmic distribution of the normalisation of…
Let $U_n=[u_{i,j}]$ be the eigenvectors matrix of a Wigner matrix. We prove that under some moments conditions, the bivariate random process indexed by $[0,1]^2$ with value at $(s,t)$ equal to the sum, over $1\le i \le ns$ and $1\le j \le…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
Local diffusion coefficients in disordered materials such as living cells are highly heterogeneous. Quenched disorder is utilized substantially to study such complex systems, whereas its analytical treatment is difficult to handle. We…
We study the distribution of resonance widths P(G) for three-dimensional (3D) random scattering media and analyze how it changes as a function of the randomness strength. We are able to identify in P(G) the system-inherent fingerprints of…
The statistics of domain walls for ground states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or…
Constructing distribution-free confidence intervals for the median, a classic problem in statistics, has seen numerous solutions in the literature. While coverage validity has received ample attention, less has been explored about interval…
Random-matrix theory is used to study the mesoscopic fluctuations of the excitation gap in a metal grain or quantum dot induced by the proximity to a superconductor. We propose that the probability distribution of the gap is a universal…
We study the effect of long range algebraic correlations on extreme value statistics and demonstrate that correlations can produce a limit distribution which is indistinguishable from the ubiquitous Bramwell-Holdsworth-Pinton distribution.…
We investigate the asymptotic behavior of the eigenvalues of the sum A+U*BU, where A and B are deterministic N by N Hermitian matrices having respective limiting compactly supported distributions \mu, \nu, and U is a random N by N unitary…
The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…