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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Projective measure without Projective Baire
投射贝尔 投射测量 勒贝格可测
2023/5/6
In this talk, I will give some of the context and a sketch of the proof of the following result which I proved a while ago: It is consistent (relative to a Mahlo catrdinal) that there is a projective ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse problem for the harmonic measure
谐波测量 反问题 双曲群
2023/4/17
Sample paths of a random walk on a hyperbolic group are known to converge to the Gromov boundary. The distribution of the exit point is called the harmonic measure. I will discuss the following invers...
Igusa's p-adic local zeta function associated to a polynomial mapping and a polynomial integration measure
Igusa's p-adic local zeta function associated polynomial mapping polynomial integration measure
2011/2/25
For p prime, we give an explicit formula for Igusa’s local zeta function associated to a polynomial mapping f = (f1, . . . , ft) : Qn p ! Qt p,with f1, . . . , ft 2 Zp[x1, . . . , xn], and an integrat...
The symmetric property tau for the Gaussian measure
The symmetric property tau the Gaussian measure
2010/11/15
We give a proof based on the Poincar\'e inequality of the symmetric property tau for the Gaussian measure. This property turns out to be equivalent to a certain functional form of the Blaschke-Santal\...
Measure valued solutions of sub-linear diffusion equations with a drift term
sublinear diffusion concentration phenomena propagation of singularities gradient flows
2010/12/9
In this paper we study nonnegative, measure valued solutions of the initial value problem for
one-dimensional drift-diffusion equations when the nonlinear diffusion is governed by an increasing C1 fu...
Brolin-Lyubich measure R of a rational endomorphism R : ˆC !ˆC with deg R 2 is the unique invariant measure of maximal entropy hR =htop(R) = log d.
Stochastic equations, flows and measure-valued processes
Stochastic equation strong solution stochasticflow coalescent generalized
2010/11/29
We first prove some general results on pathwise uniqueness,comparison property and existence of non-negative strong solutions of stochastic equations driven by white noises and Poisson random measures...
Singularities of the susceptibility of an SRB measure in the presence of stable-unstable tangencies
SRB measure stable-unstable tangencies
2010/4/1
Let $\rho$ be an SRB (or "physical"), measure for the discrete time evolution given by a map $f$, and let $\rho(A)$ denote the expectation value of a smooth function $A$. If $f$ depends on a parameter...