Related papers: Equivalence classes for large deviations
We revisit Wschebor's theorems on small increments for processes with scaling and stationary properties and deduce large deviation principles.
Differential equations where the graph of some derivative of a function is composed of a finite number of similarity transformations of the graph of the function itself are defined. We call these self-similar differential equations (SSDEs)…
Massive classification, a classification task defined over a vast number of classes (hundreds of thousands or even millions), has become an essential part of many real-world systems, such as face recognition. Existing methods, including the…
We demonstrate the large deviation property for the mild solutions of stochastic evolution equations with monotone nonlinearity and multiplica- tive noise. This is achieved using the recently developed weak convergence method, in studying…
We review and extend previous results on coincidence of mesh patterns. We introduce the notion of a force on a permutation pattern and apply it to the coincidence classification of mesh patterns, completing the classification up to size…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
This work focuses on multivalued stochastic differential equations with jumps. First, by employing the weak convergence approach, we establish the Freidlin-Wentzell uniform large deviation principle and the Dembo-Zeitouni uniform large…
We establish large deviations estimates for the largest eigenvalue of Wigner matrices with sub-Gaussian entries. Under technical assumptions, we show that the large deviation behavior of the largest eigenvalue is universal for small…
In this paper we show that the known models for $(\infty, 1)$-categories can all be extended to equivariant versions for any discrete group $G$. We show that in two of the models we can also consider actions of any simplicial group $G$.
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…
We obtain sufficient conditions ensuring the topological equivalence of two perturbed difference linear systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a…
Let a finite set of interacting particles be given, together with a symmetry Lie group $G$. Here we describe all possible dynamics that are jointly equivariant with respect to the action of $G$. This is relevant e.g., when one aims to…
The main objective of the paper is to establish explicit estimates on some applicable inequalities in two variables on time scales which can be used in the study of certain qualitative properties of dynamical equations on time scales.
We introduce an equivalence relation on $W^{s,p}({\mathbb S}^N;{\mathbb S}^N)$ involving the topological degree, and we evaluate the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. In some special…
These notes are based on the lectures that one of us (HT) gave at the Summer School on the "Theory of Large Deviations and Applications", held in July 2024 at Les Houches in France. They present the basic definitions and mathematical…
We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…
We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…
A stochastic dynamics framework for the study of complex systems is presented.
We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…