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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： On the dimension of limit sets on the real projective plane via stationary measures
实射影平面 极限集 维数 平稳测度
2023/11/29
I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the dimension of limit sets on the real projective plane via stationary measures
实射 影平面 极限集 维数 平稳测度
2023/11/15
I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Coupling by change of measures for dimension-free Harnack inequality
无维 哈纳克不等式 测度 耦合
2023/5/12
简要介绍概率论中的耦合方法及其在基础数学中的应用。引入新的变测度耦合，以简单的随机微分方程为例，将其应用于建立无穷维Harnack不等式、Bisnut导数公式和分布积分公式。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed-norm of orthogonal projections and analytic interpolation on dimensions of measures
正交投影 混合范数 度量维度 分析插值
2023/5/5
We obtain new mixed-norm estimates and geometric results on projections. In the proof we introduce a new quantity called s-amplitude, and interpolate analytically not only on p,q, but also on dimensio...
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...
Jackknife Empirical Likelihood Method for Some Risk Measures and Related Quantities
Confidence interval jackknife empirical likelihood risk measure
2016/1/20
Quantifying risks is of importance in insurance. In this paper, we employ the jackknife empirical likelihood method to construct confidence intervals for some risk measures and related quantities stud...
In this note we establish some properties of exponentiable motivic measures. As a rst
application, we show that the rationality of Kapranov's zeta function is stable under products.
As a second app...
Scalable frames are frames with the property that the frame vectors can be rescaled resulting in tight frames. However, if a frame is not scalable, one has to aim for an approximate procedure. For thi...
An important approach to establishing stochastic behavior of dynamical systems is based on the study of systems expanding a foliation and of measures having smooth densities along
the leaves of this ...
REGULARITY OF ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR PIECEWISE EXPANDING UNIMODAL MAPS
INVARIANT MEASURES UNIMODAL MAPS
2015/9/29
An important discovery of the 20th century mathematics is that many deterministic
systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
second moment but satisfying some weaker finite moment condition. For
any locally compact unimodular group G and any positive function :G→
[0,+∞], we introduce a function G, which describes the ...
Gibbs Measures and Phase Transitions on Sparse Random Graphs
Random graphs Ising model Gibbs measures Phase transitions Spin models Local weak convergence
2015/8/20
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sp...
Analysis of Performance Measures in Experimental Designs Using Jackknife
Performance Measures Experimental Designs
2015/3/20
Analysis of Performance Measures in Experimental Designs Using Jackknife.
Semispectral Measures and Feller markov Kernels
Semispectral Measure Markov Kernel C-algebras Quantum Mechanics
2012/7/11
It is well known \cite{B1,P} that a real positive semispectral measure $F$ is commutative if and only if there exist a self-adjoint operator $A$ and a Markov kernel $\mu_{(\cdot)}(\cdot):\sigma(A)\tim...
Measures of the full Hausdorff dimension for a general Sierpinski carpet
Sofic measure Sierpinski carpet matrix-valued potential Gibbs measure a-weighted thermodynamic formalism
2012/6/21
The measure of the full dimension for a general Sierpi\'{n}ski carpet is studied. In the first part of this study, we give a criterion for the measure of the full Hausdorff dimension of a Sierpi\'{n}s...