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Probability Seminar at the University of Cincinnati
Fall 2014
Sep 3, Wed, Yizao Wang
Seminar Room, French Hall 4206, 3:45-4:35pm
Title: From random partition to fractional Brownian motions.
Abstract: We review a few combinatorial stochastic processes: sampling from infinite url model (Karlin model), Chinese restaurant process, and a random graph model recently introduced by Hammond and Sheffield. Invariance principles can be established based on (modification) of these models, and fractional Brownian motions arise in the limit. If time permits, we talk about extensions to random fields.
The talk does not require any prerequisite. Joint work with Hermine Biermé and Olivier Durieu.
Sep 10, Wed, Yizao Wang
Seminar Room, French Hall 4206, 3:45-4:35pm
We continue the talk of last week. We present the ideas of the proofs.
Sep 15, Mon, 3:35-4:35, Colloquium, Joseph Najnudel, Institut de Mathématiques de Toulouse
Title: On infinite-dimensional generalization of virtual permutations
Abstract: Kerov, Olshanski and Vershik have introduced the so-called virtual permutations, defined as families of permutations (s_n)_{n >= 1} such that the cycle structure of s_n can be deduced from s_{n+1}, simply by removing n+1 from its cycle. It is possible to define a uniform measure on the space of virtual permutations. Moreover, in a joint work with A. Nikeghbali, we construct, from a random uniform virtual permutation (s_n)_{n >= 1}, a flow of operators on a suitable random functional space, which can be directly related to the limiting behavior of the cycle structure of s_n when n goes to infinity. Our construction can be extended to more general probability measures on the space of virtual permutations.
Sep 19-21, Cincinnati Symposium on Probability Theory and Applications
Sep 24, Wed, No meeting
Oct, 1, Wed, Yizao Wang
Seminar Room, French Hall 4206, 3:35-4:25pm
This talk will conclude the previous two talks on the Hammond-Sheffield model. We talk about how results can be generalized to random fields.
Oct 8, Wed, Wlodek Bryc
Seminar Room, French Hall 4206, 3:35-4:25pm
Title: Asymptotic normality of largest eigenvalue for non-centered random matrices
Oct 15, Wed, No meeting
Instead: two talks by Michael Lacey from GIT this week:
Futurama, Oct 16, Thursday, 4pm, 500 Swift Hall.
One (is the loneliest function), Oct 17, Friday, 4pm, 3220 Recreation Center.
Oct 22, Wed, David Barrera
Seminar Room, French Hall 4206, 3:35-4:25pm
Title: An Example of non-quenched Convergence in the Conditional CLT for Discrete Fourier Transforms
Abstract: A recent result by Barrera and Peligrad shows that the quenched Central Limit Theorem holds for the Fourier transforms of a stationary process in $L^2$ if a ''random'' centering is used. In this talk we show that this is a necessary condition by providing an example, in the spirit of a previous construction by Volny and Woodroofe, of a process satisfying the hypothesis of such theorem for which the discrete Fourier transforms (DFF), without random centering, do not satisfy a quenched limit theorem. The DFF of this process, by previous results by Peligrad and Wu, satisfy the corresponding CLT in the ''annealed'' sense.
Along the construction we specialize our study to the case of linear processes, which in particular brings in a discussion about 1. the representation of square-integrable periodic functions via Fourier series (and their ''stochastic'' manifestation) and 2. the Law of the Iterated Logarithm for the periodogram, both of them topics of relevance by themselves.
Oct 29, Wed, David Barrera
Seminar Room, French Hall 4206, 3:35-4:25pm
David will continue the talk from last week.
Nov 5, Wed, Ju-Yi Yen
Seminar Room, French Hall 4206, 3:35-4:25pm
Title: A different look of the Ito formula
Abstract: We introduce the concept of instant independence for certain anticipating stochastic processes and take the class of instantly independent stochastic processes as a counterpart of adapted stochastic processes for the Ito formula. Then we define the stochastic integral of a stochastic process which is a linear combination of instantly independent and adapted stochastic processes. We also show that if such decomposition exists, it is unique.
Nov 12, Wed, Magda Peligrad
Seminar Room, French Hall 4206, 3:35-4:25pm
Title: Empirical spectral distribution and spectral density.
Abstract: We form a random matrix by using independent copies of a stochastic process. Then we form the covariance matrix by multiplying with its transpose. We shall relate the limiting empirical eigenvalue distribution of the covariance matrix to the process spectral density.
Nov 19, Wed, Jacek Wesolowski, Warsaw University of Technology
Seminar Room, French Hall 4206, 3:35-4:25pm
Title: Discrete bayesian graphical models and extensions of the hyper-Dirichlet distribution
Abstract: The classical Dirichlet distribution is a familiar conjugate prior in multinomial bayesian models, when no conditional structure is imposed on the vector under study. When the conditional structure is imposed through a graph encoding conditional indpendences between components of the vector, the standard conjugate prior is hyper-Dirichlet defined by Dawid and Lauritzen (1993). Here we present an extension of hyper-Dirichlet together with new characterizations through, so called local and global independence of prameters. This characterization extends the result for the complete graph (and classical Dirichlet) proved by Geiger and Heckermann (1997). This is a joint work with Helene Massam (York Univ., Toronto, Canada).
Nov 26 Thanksgiving, No meeting
Dec 3, Wed