Related papers: Large deviation principles of one-dimensional maps…

We establish a large deviation principle (LDP) for probability graphons, which are symmetric functions from the unit square into the space of probability measures. This notion extends classical graphons and provides a flexible framework for…

We use two ingredients to prove the hyperbolicity of generic hypersurfaces of sufficiently high degree and of their complements in the complex projective space. One is the pullbacks of appropriate low pole order meromorphic jet…

This paper establishs the large deviation principle (LDP) for multiple averages on $\mathbb{N}^d$. We extend the previous work of [Carinci et al., Indag. Math. 2012] to multidimensional lattice $\mathbb{N}^d$ for $d\geq 2$. The same…

Equip the edges of the lattice $\mathbb{Z}^2$ with i.i.d. random capacities. A law of large numbers is known for the maximal flow crossing a rectangle in $\mathbb{R}^2$ when the side lengths of the rectangle go to infinity. We prove that…

Consider the random graph sampled uniformly from the set of all simple graphs with a given degree sequence. Under mild conditions on the degrees, we establish a Large Deviation Principle (LDP) for these random graphs, viewed as elements of…

The Whittaker 2d growth model is a triangular continuous Markov diffusion process that appears in many scientific contexts. It has been theoretically intriguing to establish a large deviation principle for this 2d process with a scaling…

We study Birkhoff sums as distributions. We obtain regularity results on such distributions for various dynamical systems with hyperbolicity, as hyperbolic linear maps on the torus and piecewise expanding maps on the interval. We also give…

In this note, we obtain verifiable sufficient conditions for the extreme value distribution for a certain class of skew product extensions of non-uniformly hyperbolic base maps. We show that these conditions, formulated in terms of the…

Often topological classes of one-dimensional dynamical systems are finite codimension smooth manifolds. We describe a method to prove this sort of statement that we believe can be applied in many settings. In this work we will implement it…

Given a hyperbolic homeomorphism on a compact metric space, consider the space of linear cocycles over this base dynamics which are H\"older continuous and whose projective actions are partially hyperbolic dynamical systems. We prove that…

We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…

We derive a general large deviation principle for a canonical sequence of probability measures, having its origins in random matrix theory, on unbounded sets $K$ of ${\bf C}$ with weakly admissible external fields $Q$ and very general…

We prove large deviation principles (LDPs) for random matrices in the orthogonal group and Stiefel manifold, determining both the speed and good convex rate functions that are explicitly given in terms of certain log-determinants of…

We study an inhomogeneous sparse random graph on [N] = {1, . . . , N } as introduced in a seminal paper by Bollobas, Janson and Riordan (2007): vertices have a type (here in a compact metric space S), and edges between different vertices…

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 obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…

Enumeration of various types of lattice polygons and in particular polyominoes is of primary importance in many machine learning, pattern recognition, and geometric analysis problems. In this work, we develop a large deviation principle for…

We prove two Large deviations principles (LDP) in the zone of moderate deviation probabilities. First we establish LDP for the conditional distributions of moderate deviations of empirical bootstrap measures given empirical probability…

This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…

In this paper, we give a quantitative estimate for the sum of the first $N$ Lyapunov exponents for random perturbations of a natural class $2N$-dimensional volume-preserving systems exhibiting strong hyperbolicity on a large but…