Related papers: Asymptotic equidistribution for partition statisti…

In this Ph.D dissertation (University of Virginia, 2022), we prove results about the coefficients of partition-theoretic generating functions and of coefficients of integer weight modular forms. Using various forms of the circle method, we…

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…

Recent works at the interface of algebraic combinatorics, algebraic geometry, number theory, and topology have provided new integer-valued invariants on integer partitions. It is natural to consider the distribution of partitions when…

We prove a new equidistribution estimate for the divisor function in arithmetic progression to moduli that have two small factors. We give two applications. First, we show an asymptotic formula for the divisor function over arithmetic…

Here we examine the number of ways to partition an integer $n$ into $k$th powers when $n$ is large. Simplified proofs of some asymptotic results of Wright are given using the saddle-point method, including exact formulas for the expansion…

We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…

Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…

Much like the important work of Hardy and Ramanujan proving the asymptotic formula for the partition function, Auluck and Wright gave similar formulas for unimodal sequences. Following the circle method of Wright, we provide the asymptotic…

The purpose this article is to try to understand the mysterious coincidence between the asymptotic behavior of the volumes of the Moduli Space of closed hyperbolic surfaces of genus $g$ with respect to the Weil-Petersson metric and the…

Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K.…

We employ a variant of Wright's circle method to determine the bivariate asymptotic behaviour of Fourier coefficients for a wide class of eta-theta quotients with simple poles in $\mathbb{H}$.

With tools of measure theory and symbols of matrix sequences, we explore the results regarding curves on finite fields and Weil Systems. This document wants to draw a bridge between the two areas and link the concepts of distribution of…

Asymptotic normality is frequently observed in large combinatorial structures, rigorously established for many quantities such as cycles or inversions in random permutations, the number of prime factors of random integers, and various…

We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems…

Let U be a homogeneous variety over Q of a linear algebraic group. Choose an integral model and assume the existence of infinitely many integral points. Then one would like to give an asymptotic count of integral points of bounded height…

We develop the relation between hyperbolic geometry and arithmetic equidistribution problems that arises from the action of arithmetic groups on real hyperbolic spaces, especially in dimension up to 5. We prove generalisations of Mertens'…

We study the asymptotic equidistribution of points with discrete energy close to Robin's constant of a compact set in the plane. Our main tools are the energy estimates from potential theory. We also consider the quantitative aspects of…

We propose a criterion of equidistribution by the differentiability of certain arithmetic invariants. Combined with the slope method and the asymptotic measures, this criterion gives a new "conceptual" proof to equidistribution results…

The purpose of this paper is twofold. First, we present a conjecture to the effect that the ranks of the syzygy modules of a smooth projective variety become normally distributed as the positivity of the embedding line bundle grows. Then,…

Hausel and Rodriguez-Villegas recently observed that work of G\"ottsche, combined with a classical result of Erd\H{o}s and Lehner on integer partitions, implies that the limiting Betti distribution for the Hilbert schemes…