scholarly journals Large deviation principle for one-dimensional SDEs with discontinuous coefficients

2016 ◽  
Vol 3 (2) ◽  
pp. 145-164 ◽  
Author(s):  
Alexei Kulik ◽  
Daryna Sobolieva
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Discontinuous Coefficients ◽  
One Dimensional ◽  
Deviation Principle

scholarly journals Large deviation principles of one-dimensional maps for Hölder continuous potentials

2014 ◽  
Vol 36 (1) ◽  
pp. 127-141 ◽  
Author(s):  
HUAIBIN LI
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Weak Form ◽  
Periodic Points ◽  
Hölder Continuous ◽  
One Dimensional ◽  
Deviation Principle ◽  
Large Deviation Principles ◽  
One Dimensional Maps ◽  
Level 2

We show some level-2 large deviation principles for real and complex one-dimensional maps satisfying a weak form of hyperbolicity. More precisely, we prove a large deviation principle for the distribution of iterated preimages, periodic points, and Birkhoff averages.

scholarly journals Large deviation principle in one-dimensional dynamics

2019 ◽  
Vol 218 (3) ◽  
pp. 853-888
Author(s):  
Yong Moo Chung ◽  
Juan Rivera-Letelier ◽  
Hiroki Takahasi
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
One Dimensional ◽  
Deviation Principle

scholarly journals Large Deviations and Gradient Flows for the Brownian One-Dimensional Hard-Rod System

2021 ◽  
Author(s):  
Mark Peletier ◽  
Nir Gavish ◽  
Pierre Nyquist
Keyword(s):  
Large Deviation Principle ◽  
Interacting Particle Systems ◽  
Volume Fraction ◽  
Large Deviation ◽  
Finite Size ◽  
Empirical Measure ◽  
Clear Understanding ◽  
One Dimensional ◽  
Deviation Principle ◽  
Rod System

AbstractWe study a system of hard rods of finite size in one space dimension, which move by Brownian noise while avoiding overlap. We consider a scaling in which the number of particles tends to infinity while the volume fraction of the rods remains constant; in this limit the empirical measure of the rod positions converges almost surely to a deterministic limit evolution. We prove a large-deviation principle on path space for the empirical measure, by exploiting a one-to-one mapping between the hard-rod system and a system of non-interacting particles on a contracted domain. The large-deviation principle naturally identifies a gradient-flow structure for the limit evolution, with clear interpretations for both the driving functional (an ‘entropy’) and the dissipation, which in this case is the Wasserstein dissipation. This study is inspired by recent developments in the continuum modelling of multiple-species interacting particle systems with finite-size effects; for such systems many different modelling choices appear in the literature, raising the question how one can understand such choices in terms of more microscopic models. The results of this paper give a clear answer to this question, albeit for the simpler one-dimensional hard-rod system. For this specific system this result provides a clear understanding of the value and interpretation of different modelling choices, while giving hints for more general systems.

Large deviation principle for the field in prequantum classical statistical field theory

2017 ◽  
Vol 20 (04) ◽  
pp. 1750025
Author(s):  
Andrei Khrennikov ◽  
Achref Majid
Keyword(s):  
Field Theory ◽  
Random Field ◽  
Field Model ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Background Field ◽  
Deviation Principle ◽  
Statistical Field ◽  
Statistical Field Theory

In this paper, we prove a large deviation principle for the background field in prequantum statistical field model. We show a number of examples by choosing a specific random field in our model.

scholarly journals LARGE DEVIATIONS FOR FLOWS OF INTERACTING BROWNIAN MOTIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 315-339 ◽  
Author(s):  
A. A. DOROGOVTSEV ◽  
O. V. OSTAPENKO
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Flows ◽  
Brownian Motions ◽  
Deviation Principle ◽  
And Brownian Motion

We establish the large deviation principle (LDP) for stochastic flows of interacting Brownian motions. In particular, we consider smoothly correlated flows, coalescing flows and Brownian motion stopped at a hitting moment.

scholarly journals Large Deviation Principle for the Greedy Exploration Algorithm over Erdös-Rényi Graphs

2022 ◽  
Vol 19 (1) ◽  
pp. 439
Author(s):  
Paola Bermolen ◽  
Valeria Goicoechea ◽  
Matthieu Jonckheere ◽  
Ernesto Mordecki
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Deviation Principle
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