Probability seminars 2017/2018

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Title: Jacobi triple product via the exclusion process

Speaker:    Marton Balazs (Bristol)

Date:    Wednesday, 17th January 2018

Time:    2pm

Location:    UCD, S3.56 Science South

Abstract:  I will give a brief overview of very simple, hence maybe less investigated structures in interacting particle systems: reversible product blocking measures. These turn out to be more general than most people would think, in particular asymmetric simple exclusion and nearest-neighbour asymmetric zero range processes both enjoy them. But a careful look reveals that these two are really the same process.  Exploitation of this fact will give rise to the Jacobi triple product formula - an identity previously known from number theory and combinatorics. I will derive it from pure probability this time, and I hope to surprise my audience as much as we got surprised when this identity first popped up in our notebooks.

Date: Wednesday, 24th January 2018

Time: 2pm

Location: UCD, 125 Science North (JK Lab)

Speaker: Theodoros Assiotis (Warwick)

Title: "Determinantal structures in (2+1)-dimensional growth and decay models."

Abstract: "I will talk about an inhomogeneous growth and decay model with a wall present in which the growth and decay rates on a single horizontal slice of the surface can be chosen essentially arbitrarily depending on the position. This model turns out to have a determinantal structure and most remarkably for a certain, the fully packed, initial condition the correlation kernel can be calculated explicitly in terms of one dimensional orthogonal polynomials on the positive half line and their orthogonality measures."