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The statistics of power fluctuations are studied in simulations of two-dimensional turbulence in both inverse (energy) and direct (enstrophy) cascade regimes from both Lagrangian and Eulerian perspectives. The probability density function…
In the context of first-passage percolation (FPP), we investigate the statistical properties of the selected link-times (SLTs) -the random link times comprising the optimal paths (or geodesics) connecting two given points. We focus on…
The Kardar-Parisi-Zhang (KPZ) equation is conjectured to universally describe the fluctuations of weakly asymmetric interface growth. Here we provide the first intrinsic well-posedness result for the KPZ equation on the real line by showing…
We study the probability that all eigenvalues of the Laguerre unitary ensemble of n by n matrices are between 0 and t, i.e., the largest eigenvalue distribution. Associated with this probability, in the ladder operator approach for…
For one-dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times. We argue that for self-similar growth from a single seed the…
We analyse in a systematic way the occurrences of a remarkable structure in the theory of integrable probability that we call a ``max-independence structure'', when random variables are constructed as a maximum of a sequence of independent…
This work examines various statistical distributions in connection with random Vandermonde matrices and their extension to $d$--dimensional phase distributions. Upper and lower bound asymptotics for the maximum singular value are found to…
In spite of its simplicity, the central limit theorem captures one of the most outstanding phenomena in mathematical physics, that of universality. While this classical result is well understood it is still not very clear what happens to…
We consider a last passage percolation model in dimension $1+1$ with potential given by the product of a spatial i.i.d. potential with symmetric bounded distribution and an independent i.i.d. in time sequence of signs. We assume that the…
The optimal fluctuation approach is applied to study the most distant (non-universal) tails of the free-energy distribution function P(F) for an elastic string (of a large but finite length L) interacting with a quenched random potential. A…
The probability distribution function (PDF) of the mass surface density of molecular clouds provides essential information about the structure of molecular cloud gas and condensed structures out of which stars may form. In general, the PDF…
We study the distribution of the maximal height of the outermost path in the model of $N$ nonintersecting Brownian motions on the half-line as $N\to \infty$, showing that it converges in the proper scaling to the Tracy-Widom distribution…
We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state,…
The scaling behavior of a directed polymer in a two-dimensional (2D) random potential under confining force is investigated. The energy of a polymer with configuration $\{y(x)\}$ is given by $H\big(\{y(x)\}\big) = \sum_{x=1}^N \exyx +…
We investigate properties of the particle distribution near the tip of one-dimensional branching random walks at large times $t$, focusing on unusual realizations in which the rightmost lead particle is very far ahead of its expected…
We prove the first explicit rate of convergence to the Tracy-Widom distribution for the fluctuation of the largest eigenvalue of sample covariance matrices that are not integrable. Our primary focus is matrices of type $ X^*X $ and the…
The probabilities $P_\pm(t_0,t)$ that a growing Kardar-Parisi-Zhang interface remains above or below the mean height in the time interval $(t_0, t)$ are shown numerically to decay as $P_\pm \sim (t_0/t)^{\theta_\pm}$ with $\theta_+ = 1.18…
This paper investigates the crucial role of parton distribution functions (PDFs) in high-energy physics, particularly their impact on the extraction of generalized parton distributions (GPDs) at zero skewness. To this aim, we perform six…
In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…
A theory of the probability distribution function (PDF) tails of the blob density in plasma edge turbulence is provided. A simplified model of the fast convective radial transport is used. The theoretically predicted PDF tails corroborate…