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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dean-Kawasaki equation with singular non-local interactions：well-posedness and large deviations
奇异非局部 相互作用 Dean-Kawasaki方程 适定性 大偏差
2023/11/13
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence analysis of one-point large deviations rate functions of numerical methods for stochastic wave equations with small noise
小噪声 随机波动方程 数值方法 单点大偏差率 函数收敛分析
2023/4/21
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations principle for weighted means of a recursive numerical method for ergodic SDEs
遍历 SDE递归 数值方法 加权均值 大偏差原理
2023/4/24
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements IV: the entropic repulsion phenomenon and other types of large deviations
随机交错 大偏差 熵斥力现象 大偏差
2023/5/8
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements III: Disconnection probabilities for random interlacements
随机交错 大偏差 随机交错 断开概率
2023/5/8
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements II: tilted interlacements and solidification of porous surfaces
随机交错 大偏差 倾斜交错 多孔表面 固化
2023/5/10
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements I: Large deviation principle of occupation measures
随机交错 大偏差 占用措施 大偏差原则
2023/5/10
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...
On large deviations in testing simple hypotheses for locally stationary Gaussian processes
Hypothesis testing Likelihood ratio Large deviations Locally stationary Gaussian processes Hoeffding bound Stein’s lemma Chernoff bound
2015/8/25
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...
Precise large deviations for dependent regularly varying sequences
stationary sequence large deviation principle regular variation Markov processes stochastic volatility model GARCH
2012/6/27
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) ...
Nonconventional Large Deviations Theorems
large deviations Markov processes nonconventional averages hyperbolic diffeomorphisms
2012/6/12
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 Gamma-convergence approach to large deviations
Gamma-convergence large deviations Probability
2012/4/18
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...
Large deviations for cluster size distributions in a continuous classical many-body system
Classical particle system canonical ensemble equilibrium statistical mechanics dilute system large deviations
2011/9/14
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. ...
Large deviations for truncated heavy-tailed random variables: a boundary case
heavy tails truncation regular variation large deviation
2011/9/6
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...
Effect of truncation on large deviations for heavy-tailed random vectors
heavy tails truncation regular variation large deviation
2011/9/5
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...
The asymptotic shape, large deviations and dynamical stability in first-passage percolation on cones
The asymptotic shape dynamical stability cones Probability
2011/9/2
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 ...