Related papers: Disk counting statistics near hard edges of random…
We consider the multivariate moment generating function of the disk counting statistics of a model Mittag-Leffler ensemble in the presence of a hard wall. Let $n$ be the number of points. We focus on two regimes: (a) the ``hard edge regime"…
We obtain large $n$ asymptotics for the $m$-point moment generating function of the disk counting statistics of the Mittag-Leffler ensemble. We focus on the critical regime where all disk boundaries are merging at speed…
We study the moment generating function of the disk counting statistics of a two-dimensional determinantal point process which generalizes the complex Ginibre point process. This moment generating function involves an $n \times n$…
Let $T$ be an $n\times n$ truncation of an $(n+\alpha)\times (n+\alpha)$ Haar distributed unitary matrix. We consider the disk counting statistics of the eigenvalues of $T$. We prove that as $n\to + \infty$ with $\alpha$ fixed, the…
We study the asymptotic behavior of solid partitions using transition matrix Monte Carlo simulations. If $p_3(n)$ denotes the number of solid partitions of an integer $n$, we show that $\lim_{n\rightarrow\infty} n^{-3/4} \log p_3(n)\sim…
Consider a non-negative sequence $c_n = h(n) \cdot n^{\alpha-1} \cdot \rho^{-n}$, where $h$ is slowly varying, $\alpha>0$, $0<\rho<1$ and $n\in\mathbb{N}$. We investigate the coefficients of $G(x,y) = \prod_{k\ge1}(1-x^ky)^{-c_k}$, which is…
The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter $\alpha$. For this point process, we obtain 1) exponential moment…
Assuming that a plane partition of the positive integer $n$ is chosen uniformly at random from the set of all such partitions, we propose a general asymptotic scheme for the computation of expectations of various plane partition statistics…
Let $\sum_{\beta\in\nats^d} F_\beta x^\beta$ be a multivariate power series. For example $\sum F_\beta x^\beta$ could be a generating function for a combinatorial class. Assume that in a neighbourhood of the origin this series represents a…
We introduce a dynamic random hypergraph model constructed from a bipartite graph. In this model, both vertex sets of the bipartite graph are generated by marked Poisson point processes. Vertices of both vertex sets are equipped with marks…
We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…
We derive an exact expression for the probability density of work done on a particle that diffuses in a parabolic potential with a stiffness varying by an arbitrary piecewise constant protocol. Based on this result, the work distribution…
The generating function for $p_N(n)$, the number of partitions of $n$ into at most $N$ parts, may be written as a product of $N$ factors. In part I, we studied the behavior of coefficients in the partial fraction decomposition of this…
Theory of random processes provides an attractive mathematical tool to describe the fluctuating signal from accreting sources, such as active galactic nuclei and Galactic black holes observed in X-rays. These objects exhibit featureless…
We study pair correlation functions for planar Coulomb systems in the pushed phase, near a ring-shaped impenetrable wall. We assume coupling constant $\Gamma=2$ and that the number $n$ of particles is large. We find that the correlation…
In this paper, we derive non-asymptotic achievability and converse bounds on the random number generation with/without side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on…
Consider a stationary Poisson point process in $\mathbb{R}^d$ and connect any two points whenever their distance is less than or equal to a prescribed distance parameter. This construction gives rise to the well known random geometric…
We simulate a model of self-propelled disks with soft repulsive interactions confined to a box in two dimensions. For small rotational diffusion rates, monodisperse disks spontaneously accumulate at the walls. At low densities, interaction…
Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…
In the present paper we calculate explicitly the constant factor $C$ in the large $N$ asymptotics of the partition function $Z_N$ of the six-vertex model with domain wall boundary conditions on the critical line between the disordered and…