Related papers: Sample path large deviations for queueing networks…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from…
Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We obtain sample-path large deviations for scaled processes $\bar X_n(t) \triangleq X(nt)/n$ and obtain a similar result for random walks. Our results yield detailed…
We find large deviations rates for consensus-based distributed inference for directed networks. When the topology is deterministic, we establish the large deviations principle and find exactly the corresponding rate function, equal at all…
A classic network tomography problem is estimation of properties of the distribution of route traffic volumes based on counts taken on the network links. We consider inference for a general class of models for integer-valued traffic. Model…
A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…
Subsequence-based time series classification algorithms provide accurate and interpretable models, but training these models is extremely computation intensive. The asymptotic time complexity of subsequence-based algorithms remains a…
In this paper, a many-sources large deviations principle (LDP) for the transient workload of a multi-queue single-server system is established where the service rates are chosen from a compact, convex and coordinate-convex rate region and…
In this work, we study large deviation properties of the covariance process in fully connected Gaussian deep neural networks. More precisely, we establish a large deviation principle (LDP) for the covariance process in a functional…
We prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations with monotone drifts, which in particular contains a class of SDEs with reflection in a convex domain.
A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to…
We prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large…
We study large deviations in the context of stochastic gradient descent for one-hidden-layer neural networks with quadratic loss. We derive a quenched large deviation principle, where we condition on an initial weight measure, and an…
Neural networks are known to give better performance with increased depth due to their ability to learn more abstract features. Although the deepening of networks has been well established, there is still room for efficient feature…
We study the statistical properties of the sampled scale-free networks, deeply related to the proper identification of various real-world networks. We exploit three methods of sampling and investigate the topological properties such as…
Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…
We establish large deviation principles for the largest eigenvalue of large random matrices with variance profiles. For $N \in \mathbb N$, we consider random $N \times N$ symmetric matrices $H^N$ which are such that…
We establish a large deviation principle for time dependent trajectories (paths) of the empirical density of $N$ particles with long range interactions, for homogeneous systems. This result extends the classical kinetic theory that leads to…
Consider a real diagonal deterministic matrix $X_n$ of size $n$ with spectral measure converging to a compactly supported probability measure. We perturb this matrix by adding a random finite rank matrix, with delocalized eigenvectors. We…
Distributions of the resilience of transport networks are studied numerically, in particular the large-deviation tails. Thus, not only typical quantities like average or variance but the distributions over the (almost) full support can be…