Related papers: Random Partitions and Cohen-Lenstra Heuristics
We extend the definition of the Lerch distribution to the set of nonnegative integers for greater applicability to modeling count data. We express its properties in terms of Lerch's transcendent, and study its unimodality, hazard function…
The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.
We propose a refinement of the random matrix model for a certain family of $L$-functions over $\mathbb F_q[u]$, using techniques that we hope will eventually apply to an arbitrary family of $L$-functions. This consists of a probability…
In this paper we investigate the distribution properties of hybrid sequences which are made by combining Halton sequences in the ring of polynomials and digital Kronecker sequences. We give a full criterion for the uniform distribution and…
Given a finite abelian group $\Gamma$, we study the distribution of the $p$-part of the class group $\operatorname{Cl}(K)$ as $K$ varies over Galois extensions of $\mathbb{Q}$ or $\mathbb{F}_q(t)$ with Galois group isomorphic to $\Gamma$.…
In this paper we make a series of numerical experiments to support Greenberg's $p$-rationality conjecture, we present a family of $p$-rational biquadratic fields and we find new examples of $p$-rational multiquadratic fields. In the case of…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
The family of skew-symmetric distributions is a wide set of probability density functions obtained by combining in a suitable form a few components which are selectable quite freely provided some simple requirements are satisfied. Intense…
This is an extended and corrected version of the author's Diplomarbeit. A class of algebras called generic pro-$p$ Hecke algebras is introduced, enlarging the class of generic Hecke algebras by considering certain extensions of (extended)…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold…
Operators acting on the discrete random chaos yield signed multiplicative systems, extending the notion of spin matrices and quaternions. We investigate signed groups through the associated sign matrices, focusing on generators and their…
In this note we will discuss a potentially interesting extension of some recent results on primitive solutions to completely integrable partial differential equations. We will discuss a family distributions that are holomorphic on the…
New criteria are shown that certain combinations of finite unimodal polynomials are unimodal. %Given unimodal polynomials with explicit expressions and dependent recursion relations, we propose an approach to determine their modes. As…
Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg's…
A multifractal analysis is performed on the universality classes of random matrices and the transition ones.Our results indicate that the eigenvector probability distribution is a linear sum of two chi-squared distribution throughout the…
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…
We consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory. These ensembles occur in certain problems in combinatorial probability and can be thought of…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…