Related papers: Fluctuations in the random-link matching problem
In recent years, large language models (LLMs) have demonstrated remarkable capabilities in comprehending and generating natural language content, attracting widespread attention in both industry and academia. An increasing number of…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…
These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…
This PhD thesis is organized as follows. In the first two chapters I will review some basic notions of statistical physics of disordered systems, such as random graph theory, the mean-field approximation, spin glasses and combinatorial…
Consider a polynomial optimisation problem, whose instances vary continuously over time. We propose to use a coordinate-descent algorithm for solving such time-varying optimisation problems. In particular, we focus on relaxations of…
The common way to optimize auction and pricing systems is to set aside a small fraction of the traffic to run experiments. This leads to the question: how can we learn the most with the smallest amount of data? For truthful auctions, this…
The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti and M. M\'ezard [Eur. Phys. B. 57, 175…
This paper presents an in-depth mathematical analysis of the Monte Carlo replica method, commonly used in global fitting studies within the high-energy physics theory field. For the first time, we offer a rigorous derivation of the…
Modern stochastic optimization methods often rely on uniform sampling which is agnostic to the underlying characteristics of the data. This might degrade the convergence by yielding estimates that suffer from a high variance. A possible…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
We consider the Random Euclidean Assignment Problem in dimension $d=1$, with linear cost function. In this version of the problem, in general, there is a large degeneracy of the ground state, i.e. there are many different optimal matchings…
We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in the case where the random walk terminates at some boundary. We recently found…
Numerical computing of the rank of a matrix is a fundamental problem in scientific computation. The datasets generated by the internet often correspond to the analysis of high-dimensional sparse matrices. Notwithstanding recent advances in…
The ``Brownian bees'' model describes an ensemble of $N=$~const independent branching Brownian particles. The conservation of $N$ is provided by a modified branching process. When a particle branches into two particles, the particle which…
In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realise large-deviation events. The bias acts on a single…
We introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities, such as current or density, that are local in time. The large-deviation functions are given in terms of the typical…
Fluctuation scaling is observed phenomenon from complex networks through finance to ecology. It means that the variance and the mean of a specific quantity are related as $\ev{\sigma^2|n}\propto \ev{n|A}^{2\alpha}$ with $1/2\geq \alpha \geq…
A large deviation principle is established for a general class of stochastic flows in the small noise limit. This result is then applied to a Bayesian formulation of an image matching problem, and an approximate maximum likelihood property…
We consider a discrete-time random walk on a one-dimensional lattice with space and time-dependent random jump probabilities, known as the Beta random walk. We are interested in the probability that, for a given realization of the jump…