概率论

We present an optimization-based formulation of the Red Light Green Light (RLGL) algorithm for computing stationary distributions of large Markov chains. This perspective clarifies the algorithm's behavior, establishes exponential…

We describe the large deviations above its typical value of the maximal energy of a spin glass with +/-1 spins. Thanks to the relatively explicit description of the rate function we identify, we then show that the latter is asymptotically…

Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the degree distribution follows a power-law, capturing the…

In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a…

We introduce the Random Quadratic Form (RQF): a stochastic differential equation which formally corresponds to the gradient flow of a random quadratic functional on a sphere. While the one-point dynamics of the system is a Brownian motion…

Let $(X, \mfA,P)$, $(Y, \mfB,Q)$ be two arbitrary probability spaces and $\P:=\{(\mfA,P_y):y\in{Y}\}$ be a regular conditional probability on $\mfA$ with respect to $Q$. Denote by $R$ the skew product of $P$ and $Q$ determined by…

While suitably scaled CNNs with Gaussian initialization are known to converge to Gaussian processes as the number of channels diverges, little is known beyond this Gaussian limit. We establish a large deviation principle (LDP) for…

Gurau (2020) proposed a generalization of the trace of the matrix resolvent to tensors of higher order, and recent work has explored analogs of the Wigner semicircle and Marchenko-Pastur distributions from random matrix theory as well as…

We study a multivariate Hawkes process with long-range interactions, where the interaction strength decays as a power-law in the distance of the particles with exponent $1+\alpha.$ Our main focus is on the long-time asymptotic behavior of…

We consider the Sherrington--Kirkpatrick spin glass model with zero external field and at inverse temperature $\beta>0$. Let $F_N(\beta)$ be the corresponding log-partition function. Under the assumption that $c_N:=N^{1/3}(1-\beta_N^2)$ is…

In this paper, we consider a once-reinforced random walk on the half-line, and give the limiting behaviors of all the moments of its range.

We consider Bernoulli percolation on $\mathbb Z^d$ with $d>6$. We prove an up-to-constant estimate for the critical two-point function restricted to a half-space. This completes previous results of Chatterjee and Hanson (Commun. Pure Appl.…

We study the Bergman determinantal point process from a theoretical point of view motivated by its simulation. We construct restricted and restricted-truncated variants of the Bergman kernel and show optimal transport inequalities involving…

This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…

This paper addresses the existence and uniqueness of solutions to Reflected Generalized Backward Stochastic Differential Equations (GRBSDEs) within a general filtration that supports a Brownian motion and an independent integer-valued…

This paper establishes an equilibrium existence result for a class of Mean Field Games involving Reflected Stochastic Differential Equations. The proof relies on the framework of relaxed controls and martingale problems.

We consider a system of two stochastic differential equations (SDEs) with competing two-way interactions driven by Brownian motions and spectrally positive $\alpha$-stable random measures. Such a SDE system can be identified as a…

A family of random matrices $\boldsymbol{X}^N=(X_1^N,\ldots,X_d^N)$ is said to converge strongly to a family of bounded operators $\boldsymbol{x}=(x_1,\ldots,x_d)$ when $\|P(\boldsymbol{X}^N,\boldsymbol{X}^{N*})\|\to\|P(\boldsymbol{x},…

We consider the sets of negatively associated (NA) and negatively correlated (NC) distributions as subsets of the space $\mathcal{M}$ of all probability distributions on $\mathbb{R}^n$, in terms of their relative topological structures…

We study the local limits of uniform random triangulations with boundaries in the regime where the genus is proportional to the number of faces. Budzinski and Louf proved in 2020 that when there are no boundaries, the local limits exist and…