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Recent studies show that transformer-based architectures emulate gradient descent during a forward pass, contributing to in-context learning capabilities - an ability where the model adapts to new tasks based on a sequence of prompt…
In many interacting particle systems, relaxation to equilibrium is thought to occur via the growth of 'droplets', and it is a question of fundamental importance to determine the critical length at which such droplets appear. In this paper…
In comparing the behavior of an energy spectrum to the predictions of random matrix theory one must transform the spectrum such that the averaged level spacing is constant, a procedure known as unfolding. Once energy spectrums belong to an…
Define the scaled empirical point process on an independent and identically distributed sequence $\{Y_i: i\le n\}$ as the random point measure with masses at $a_n^{-1} Y_i$. For suitable $a_n$ we obtain the weak limit of these point…
The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…
Due to the potential application of regulating droplet shape by external fields in microfluidic technology and micro devices, it becomes increasingly important to understand the shape formation of a droplet in the presence of an electric…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
Recently, the joint probability density functions of complex eigenvalues for products of independent complex Ginibre matrices have been explicitly derived as determinantal point processes. We express truncated series coming from the…
In this paper, we study the perturbation of the extreme singular values of a matrix in the particular case where it is obtained after appending an arbitrary column vector. Such results have many applications in bifurcation theory, signal…
We prove nonasymptotic matrix concentration inequalities for the spectral norm of (sub)gaussian random matrices with centered independent entries that capture fluctuations at the Tracy-Widom scale. This considerably improves previous bounds…
We discuss a method of the asymptotic computation of moments of the normalized eigenvalue counting measure of random matrices of large order. The method is based on the resolvent identity and on some formulas relating expectations of…
For a broad class of unitary ensembles of random matrices we demonstrate the universal nature of the Janossy densities of eigenvalues near the spectral edge, providing a different formulation of the probability distributions of the limiting…
We are concerned with the problem of detecting a single change point in the model parameters of time series data generated from an exponential family. In contrast to the existing literature, we allow that the true location of the change…
Let $A$ be an $n \times n$ random matrix with iid entries over a finite field of order $q$. Suppose that the entries do not take values in any additive coset of the field with probability greater than $1 - \alpha$ for some fixed $0 < \alpha…
It has been recently discovered that some random processes may satisfy limit theorems even though they exhibit intermittency, namely an unusual growth of moments. In this paper we provide a deeper understanding of these intricate limiting…
This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…