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

Fall 2016

7 Sep Axel Saenz (UVA)
Plancherel Growth Process and Integrability
26 Oct Alisa Knizel (MIT)
Asymptotics of random domino tilings of rectangular Aztec diamonds.
* please note time, date, and/or location change

Abstracts

Plancherel Growth Process and Integrability

Axel Saenz (UVA)

The Plancherel Growth process is a Markov process on Young diagrams. In this talk, I will write a generating function of the transition probabilities of the process and relate this function to theory of KP integrability. This integrability hierarchy gained popularity with Japanese school in the early 80's within the context of Soliton waves and it also had a resurgence in the mid 90's with the intersection numbers of the moduli space of curves. Now, there seems to be an interaction between probabilistic models and integrability which allows for beautiful, interesting, and exact formulas. This is a result in that direction.
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Asymptotics of random domino tilings of rectangular Aztec diamonds

Alisa Knizel (UVA)

We consider global asymtotics of a domino tiling model on a class of domains which we call rectangular Aztec diamonds. We prove the Law of Large Numbers for the corresponding height functions, provide explicit formulas for the limit and compute the frozen boundary for a large class of examples. We also establish the convergence of the fluctuations to the Gaussian Free Field in appropriate coordinates. Our main tool is a recently developed moment method for discrete particle systems.
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Mathematics Recent Seminars Other Seminars Maps & Directions