Related papers: Logarithmic potential theory and large deviation

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…

We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…

A general theory based upon 7 postulates is introduced. The basical notions are theoretical variables that are associated with an observer or with a group of communicating observers. These variables may be accessible or inaccessible. From…

We prove a large deviation principle for the point process associated to $k$-element connected components in $\mathbb R^d$ with respect to the connectivity radii $r_n\to\infty$. The random points are generated from a homogeneous Poisson…

In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a…

Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…

We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages $\frac{1}{|\Lambda|} \sum_{i\in\Lambda} X_i$, where the $X_i$'s are copies of a…

Large deviation theory quantifies the occurence of events that deviate from the average behavior of a system. Such events arise from non-typical trajectories of the dynamics. In this note we derive the time evolution of these rare…

We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…

Establishing a Large Deviation Principle (LDP) proves to be a powerful result for a vast number of stochastic models in many application areas of probability theory. The key object of an LDP is the large deviations rate function, from which…

We demonstrate the large deviation principle in the small noise limit for the three dimensional stochastic planetary geostrophic equations of large-scale ocean circulation. In this paper, we first prove the well-posedness of weak solutions…

This paper studies large deviation principles and weak convergence, both at the level of finite-dimensional distributions and in functional form, for a class of continuous, isotropic, centered Gaussian random fields defined on the unit…

We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and…

A two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged regular closed region K whose charge density is determined by its equilibrium potential at an inverse…

We prove a full large deviations principle in large time, for a diffusion process with random drift V, which is a centered Gaussian shear flow random field. The large deviations principle is established in a ``quenched'' setting, i.e. is…

Quantum theory combines density matrices, Born probabilities, tensor-product composites, positive-operator-valued measures (POVMs), and quantum channels. In a finite-dimensional causal operational theory, we prove that two postulates…

We establish large deviation principles for the couple of the maximum likelihood estimators of dimensional and drift coefficients in the generalised squared radial Ornstein-Uhlenbeck process. We focus our attention to the most tractable…

The aim of this note is to announce some results about the probabilistic and deterministic asymptotic properties of linear groups. The first one is the analogue, for norms of random matrix products, of the classical theorem of Cramer on…

For Y a subset of the complex plane,a beta ensemble is a sequence of probability measures on Y^n for n=1,2,3...depending on a real-valued continuous function Q and a real positive parameter beta.We consider the associated sequence of…

Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…