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We go through Zimmer's book Chapter 2-3, making some preparations for Margulis super-rigidity theorem.
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...
Modeling non-commutative phenomena in finite dimensional matrix algebras is a central theme of the program Quantitative Linear Algebra. This workshop will focus on a variety of concrete questions aro...
This paper investigates front propagation in random media for a free boundary problem arising in combustion theory. We show the existence of asymptotic travelling waves solutions with effective speedd...
We consider a process on T2, which consists of fast motion along the stream lines of an incompressible periodic vector field perturbed by white noise. It gives rise to a process on the graph n...
For n > 2, the action of the outer automorphism group of the rank n free group Fn on Hom(Fn, SU(2))/SU(2) is ergodic with respect to the Lebesgue measure class.
We consider a process on T 2, which consists of the fast motion along the stream lines of an incompressible periodic vector field perturbed by white noise. It gives rise to a process on the grap...
We consider the cutoff phenomenon in the context of families of ergodic Markov transition functions. This includes classical examples such as families of ergodic finite Markov chains and Brownian mo...
A key result underlying the theory of MCMC is that any η-irreducible Markov chain having a transition density with respect to η and possessing a stationary distribution is automatically positive Harri...
The Foundational Role of Ergodic Theory.
We consider the problem of the construction of the asymptotically distribution free test by the observations of ergodic diffusion process. It is supposedd that under the basic hypothesis the trend coe...
We consider the problem of the construction of the asymptotically distribution free test by the observations of ergodic diffusion process. It is supposedd that under the basic hypothesis the trend coe...
In [Chen, D., Owen, Ann. Stat., 39, 673--701, 2011] Markov chain Monte Carlo (MCMC) was studied under the assumption that the driver sequence is a deterministic sequence rather than independent U(0,1)...
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we c...

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