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We propose a method for determining the most likely cause, in terms of conventional generator outages and renewable fluctuations, of power system frequency reaching a predetermined level that is deemed unacceptable to the system operator.…

Systems and Control · Electrical Eng. & Systems 2020-05-26 Brendan Patch , Bert Zwart

We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof…

Probability · Mathematics 2010-12-14 Magdalena Kobylanski

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…

Probability · Mathematics 2018-02-02 Mauro Mariani

Let d \geq d_0 be a sufficiently large constant. A (n,d,c \sqrt{d}) graph G is a d-regular graph over n vertices whose second largest (in absolute value) eigenvalue is at most c \sqrt{d}. For any 0 < p < 1, G_p is the graph induced by…

Probability · Mathematics 2007-05-23 Eran Ofek

We study the giant component problem slightly above the critical regime for percolation on Poissonian random graphs in the scale-free regime, where the vertex weights and degrees have a diverging second moment. Critical percolation on…

Probability · Mathematics 2021-07-12 Souvik Dhara , Remco van der Hofstad

We study the probability distribution $P$ of the sum of a large number of non-identically distributed random variables $n_m$. Condensation of fluctuations, the phenomenon whereby one of such variables provides a macroscopic contribution to…

Statistical Mechanics · Physics 2016-04-29 Federico Corberi

We consider the supercritical bond percolation on $\mathbb Z^d$ and study the graph distance on the percolation graph called the chemical distance. It is well-known that there exists a deterministic constant $\mu(x)$ such that the chemical…

Probability · Mathematics 2023-04-12 Barbara Dembin , Shuta Nakajima

As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two $k$-cliques means that they share at least $l<k$ vertices. In this paper, we develop a theoretical…

Statistical Mechanics · Physics 2015-10-09 Ming Li , Youjin Deng , Bing-Hong Wang

We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…

Probability · Mathematics 2007-12-05 Boualem Djehiche , Jens Svensson

We present an analytical technique to compute the probability of rare events in which the largest eigenvalue of a random matrix is atypically large (i.e.\ the right tail of its large deviations). The results also transfer to the left tail…

Statistical Mechanics · Physics 2021-05-26 Antoine Maillard

We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…

Probability · Mathematics 2025-12-23 Joost Jorritsma , Pascal Maillard , Peter Mörters

In this paper, the large deviations on trajectory level for ergodic Markov processes are studied. These processes take values in the non-negative quadrant of the two dimension lattice and are concentrated on step-wise functions. The rates…

Probability · Mathematics 2013-10-22 A. Mogulskii , E. Pechersky , A. Yambartsev

We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…

Probability · Mathematics 2007-05-23 Christina Goldschmidt

We study the distribution of the time-integrated current in an exactly-solvable toy model of heat conduction, both analytically and numerically. The simplicity of the model allows us to derive the full current large deviation function and…

Statistical Mechanics · Physics 2009-11-13 Pablo I. Hurtado , Pedro L. Garrido

We show that large deviation properties of Erd\"os-R\'enyi random graphs can be derived from the free energy of the $q$-state Potts model of statistical mechanics. More precisely the Legendre transform of the Potts free energy with respect…

Statistical Mechanics · Physics 2009-11-10 Andreas Engel , Rémi Monasson , Alexander K. Hartmann

In this paper, we present large deviation theory that characterizes the exponential estimate for rare events of stochastic dynamical systems in the limit of weak noise. We aim to consider next-to-leading-order approximation for more…

Machine Learning · Statistics 2023-06-21 Yang Li , Shenglan Yuan , Linghongzhi Lu , Xianbin Liu

Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…

Statistical Mechanics · Physics 2017-03-21 Corentin Herbert

In this paper, we study the critical behavior of percolation on a configuration model with degree distribution satisfying an infinite second-moment condition, which includes power-law degrees with exponent $\tau \in (2,3)$. It is well known…

Probability · Mathematics 2020-07-01 Souvik Dhara , Remco van der Hofstad , Johan S. H. van Leeuwaarden

In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…

Probability · Mathematics 2009-08-21 Henrik Hult , Gennady Samorodnitsky

Large fluctuations have received considerable attention as they encode information on the fine-scale dynamics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermodynamical properties. Here we…

Statistical Mechanics · Physics 2010-12-09 David Andrieux