UVA Probability Seminar
Wednesdays, 4:30 - 5:30pm
Kerchof 317
Organizers: Christian Gromoll, Tai Melcher, & Leonid Petrov
Mathematics Recent Seminars Other Seminars Maps & Directions

Spring 2015

28 Jan Natasha Blitvic (Indiana)
Segal-Bargmann Transform in Non-commutative Probability
18 Feb [CANCELLED] Anirban Basak (Duke)
Talk canceled due to weather
25 Mar Vadim Gorin (MIT)
Multilevel Dyson Brownian Motion and its edge limits
1 Apr Nathan Glatt-Holtz (Virginia Tech)
Stochastic PDEs and Turbulence
22 Apr Naya Bhatnagar (U Delaware)
Lengths of Monotone Subsequences in a Mallows Permutation
* please note time, date, and/or location change

Abstracts

Segal-Bargmann Transform in Non-commutative Probability

Natasha Blitvic (Indiana)

I will give an introduction to non-commutative probability, a vibrant area at the interface of (classical) probability, operator algebras, combinatorics, and mathematical physics. We will discuss some ways in which the non-commutative theory parallels and contrasts with the classical theory. The motivation will be the recent joint work with T. Kemp on the extension of the Segal-Bargmann analysis to an interesting two-parameter family of non-commutative probability spaces.
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Multilevel Dyson Brownian Motion and its edge limits

Vadim Gorin (MIT)

The GUE Tracy-Widom distribution is known to govern the large-time asymptotics for a variety of interacting particle systems on one side, and the asymptotic behavior for largest eigenvalues of random Hermitian matrices on the other side. In my talk I will explain some reasons for this connection between two seemingly unrelated classes of stochastic systems, and how this relation can be extended to general beta random matrices. A multilevel extension of the Dyson Brownian Motion will be the central object in the discussion. (Based on joint papers with Misha Shkolnikov).
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Stochastic PDEs and Turbulence

Nathan Glatt-Holtz (Virginia Tech)

I will survey some recent results concerning the ergodic theory of nonlinear stochastic PDEs and describe how these results have bearing on various statistical theories of turbulent fluid flow.
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Lengths of Monotone Subsequences in a Mallows Permutation

Naya Bhatnagar (U Delaware)

The longest increasing subsequence (LIS) of a uniformly random permutation is a well studied problem. Vershik-Kerov and Logan-Shepp first showed that asymptotically the typical length of the LIS is 2sqrt(n). This line of research culminated in the work of Baik-Deift-Johansson who related this length to the Tracy-Widom distribution.

We study the length of the LIS and LDS of random permutations drawn from the Mallows measure, introduced by Mallows in connection with ranking problems in statistics. Under this measure, the probability of a permutation p in S_n is proportional to q^{Inv(p)} where q is a real parameter and Inv(p) is the number of inversions in p. We determine the typical order of magnitude of the LIS and LDS, large deviation bounds for these lengths and a law of large numbers for the LIS for various regimes of the parameter q.

This is joint work with Ron Peled.
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Mathematics Recent Seminars Other Seminars Maps & Directions