Related papers: Large random matrices with given margins
Patterned random matrices such as the reverse circulant, the symmetric circulant, the Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD), have attracted much attention. Under the assumption that the…
At the core of modern generative modeling frameworks, including diffusion models, score-based models, and flow matching, is the task of transforming a simple prior distribution into a complex target distribution through stochastic paths in…
This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated boundary conditions in this formalism. In…
This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…
We develop a class of exponential bounds for the probability that a martingale sequence crosses a time-dependent linear threshold. Our key insight is that it is both natural and fruitful to formulate exponential concentration inequalities…
The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…
For a class of symmetric random matrices whose entries are martingale differences adapted to an increasing filtration, we prove that under a Lindeberg-like condition, the empirical spectral distribution behaves asymptotically similarly to a…
Permanents of random matrices with independent and identically distributed (i.i.d.) entries have extensively studied in literature and convergence and concentration properties are known under varying assumptions on the distributions. In…
We compute the limiting statistical distribution of the eigenvalues of sequences of matrices whose entries satisfy what we call a vanishing mean variation condition and are $\mu$-distributed for some probability measure. As an application…
We study the Schr\"odinger bridge problem when the endpoint distributions are available only through samples. Classical computational approaches estimate Schr\"odinger potentials via Sinkhorn iterations on empirical measures and then…
An $n \times n$ matrix with $\pm 1$ entries which acts on $\mathbb{R}^n$ as a scaled isometry is called Hadamard. Such matrices exist in some, but not all dimensions. Combining number-theoretic and probabilistic tools we construct matrices…
This paper develops an optimal Chernoff type bound for the probabilities of large deviations of sums $\sum_{k=1}^n f (X_k)$ where $f$ is a real-valued function and $(X_k)_{k \in \mathbb{Z}_{\ge 0}}$ is a finite state Markov chain with an…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
In this paper, we show a large deviation principle for certain sequences of static Schr\"{o}dinger bridges, typically motivated by a scale-parameter decreasing towards zero, extending existing large deviation results to cover a wider range…
We perform numerical studies including Monte Carlo simulations of high rotational symmetry random tilings. For computational convenience, our tilings obey fixed boundary conditions in regular polygons. Such tilings are put in correspondence…
We present a randomized approximation algorithm for counting contingency tables, mxn non-negative integer matrices with given row sums R=(r_1, ..., r_m) and column sums C=(c_1, ..., c_n). We define smooth margins (R,C) in terms of the…
Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained from X by dividing each row of X by its sum.…
Schr\"odinger bridges have emerged as an enabling framework for unveiling the stochastic dynamics of systems based on marginal observations at different points in time. The terminology "bridge'' refers to a probability law that suitably…