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The Dean-Kawasaki equation with non-local singular interactions and correlated noise will be introduced, which describes the evolution of the density function for a system of finitely many particles g...
In this talk, we present the pointwise convergence of one-point large deviations rate functions (LDRFs) of the spatial finite difference method and further the fully discrete method based on the tempo...
For ergodic SDEs, their ergodic limits are usually approximated by the suitable means of numerical methods. To reveal the numerical asymptotic behavior, we study the large deviations principle (LDP) f...
In this lecture, I will talk about how to control the deviation of the occupation-time profile conditioned on disconnection so that this conditioning makes the model exhibit a phenomenon generally kno...
In this lecture, I will discuss how ``tilted interlacements’’ and ``solidification of porous surfaces’’, two specific realizations of the change-of-measure and coarse graining ideas respectively, prod...
In this lecture, I will discuss how tilting and coarse graining, two key ideas in modern probability, come into play in deriving respectively the lower and upper bounds of the asymptotic probability i...
In this lecture, I will talk about the large deviation problems in random interlacements, in particular the LDP of the occupation measure, and discuss its relations to sharp asymptotic probabilities o...
We derive a large deviation result for the log-likelihood ratio for testing simple hypotheses in locally stationary Gaussian processes. This result allows us to find explicitly the rates of exponentia...
We study a precise large deviation principle for a stationary regularly varying sequence of random variables. This principle extends the classical results of A.V. Nagaev (1969) and S.V. Nagaev (1979) ...
We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hy...
A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable map...
Abstract: An interesting problem in statistical physics is the condensation of classical particles in droplets or clusters when the pair-interaction is given by a stable Lennard-Jones-type potential. ...
Abstract: This paper investigates the decay rate of the probability that the row sum of a triangular array of truncated heavy tailed random variables is larger than an integer (k) times the truncating...
Abstract: This paper studies the effect of truncation on the large deviations behavior of the partial sum of a triangular array coming from a truncated power law model. Each row of the triangular arra...
Abstract: In this paper we consider first-passage percolation on certain subgraphs of the $\Z^d$ nearest neighbour graph. We present a three-fold extension of the Shape Theorem. Firstly, we show that ...

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