相关论文: The distribution of values in the quadratic assign…

We consider three classes of linear differential equations on distribution functions, with a fractional order $\alpha\in [0,1].$ The integer case $\alpha =1$ corresponds to the three classical extreme families. In general, we show that…

We solve the secretary problem in the case that the ranked items arrive in a statistically biased order rather than in uniformly random order. The bias is given by the left-to-right-minimum exponentially tilted distribution with parameter…

An involution is a bijection that is its own inverse. Given a permutation $\sigma$ of $[n],$ let $\mathsf{invol}(\sigma)$ denote the number of ways $\sigma$ can be expressed as a composition of two involutions of $[n].$ We prove that the…

We consider a special family of Gaussian hypergeometric functions whose entries are cubic and trivial characters over finite fields. The special values of these functions are known to give the Frobenius traces of families of Hessian…

Let $S_n$ be the symmetric group on the set $\{1,2,\ldots,n\}$. Given a permutation $\sigma=\sigma_1\sigma_2 \cdots \sigma_n \in S_n$, we say it has a peak at index $i$ if $\sigma_{i-1}<\sigma_i>\sigma_{i+1}$. Let $\text{Peak}(\sigma)$ be…

Encouraged by the study of extremal limits for sums of the form $$\lim_{N\to\infty}\frac{1 }{N}\sum_{n=1}^N c(x_n,y_n)$$ with uniformly distributed sequences $\{x_n\},\,\{y_n\}$ the following extremal problem is of interest…

We show that the average cost for the traveling-salesman problem in two dimensions, which is the archetypal problem in combinatorial optimization, in the bipartite case, is simply related to the average cost of the assignment problem with…

Eigenvalue distributions are important dynamical quantities in matrix models, and it is an interesting challenge to study corresponding quantities in tensor models. We study real tensor eigenvalue/vector distributions for real symmetric…

By using the independence structure of points following a determinantal point process, we study the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameter n and k. The…

We consider a discrete time random walk in one dimension. At each time step the walker jumps by a random distance, independent from step to step, drawn from an arbitrary symmetric density function. We show that the expected positive maximum…

We consider the asymptotic distribution of the IP sparsity function, which measures the minimal support of optimal IP solutions, and the IP to LP distance function, which measures the distance between optimal IP and LP solutions. We create…

Let $A$ be a real skew-symmetric Gaussian random matrix whose upper triangular elements are independently distributed according to the standard normal distribution. We provide the distribution of the largest singular value $\sigma_1$ of…

We prove several general formulas for the distributions of various permutation statistics over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formulas involve certain kinds of plethystic…

We propose a numerical algorithm for computing approximately optimal solutions of the matching for teams problem. Our algorithm is efficient for problems involving large number of agent categories and allows for non-discrete agent type…

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…

In this paper, we investigate the eigenvalue distribution of a class of kernel random matrices whose $(i,j)$-th entry is $f(X_i,X_j)$ where $f$ is a symmetric function belonging to the Paley-Wiener space $\mathcal{B}_c$ and $(X_i)_{1\leq i…

We initiate the study of fair distribution of delivery tasks among a set of agents wherein delivery jobs are placed along the vertices of a graph. Our goal is to fairly distribute delivery costs (modeled as a submodular function) among a…

Routing problems are a common optimization problem in industrial applications, which occur on a large scale in supply chain planning. Due to classical limitations for solving NP-hard problems, quantum computing hopes to improve upon speed…

Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel…

We study the distribution functions of several classical error terms in analytic number theory, focusing on the remainder term in the Dirichlet divisor problem $\Delta(x)$. We first bound the discrepancy between the distribution function of…