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North British Probability Seminar

North British Probability Seminar

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North British Probability Seminar – Events

Upcoming Seminars and Events: (NBPS runs on Tuesday afternoons from 3.05 pm to 4 pm this academic year)

 

Tuesday, July 2, 2024

Kilian Raschel (Université d’Angers)

Time: 3.05 pm, Tuesday, July 2, 2024

Location: JCMB 5323

Zoom link:  https://ed-ac-uk.zoom.us/j/81912013907

Meeting ID:  819 1201 3907

Passcode: nbps2023

Title: A functional equation approach to reflected Brownian motion
Abstract:

The last two decades have seen a flurry of activity around the combinatorial model of walks in the quarter plane. One reason for this is that this model not only occupies a central position in enumerative combinatorics (via bijections with other combinatorial models), but it has also motivated different communities (probability, complex analysis, functional equations, Galois theory, etc.) to work together to develop new techniques and derive new results. While it can be said that walks in the quarter plane are now fairly well understood, a natural question for a probabilist is to study the continuous analogue, namely Brownian motion in a quadrant. It turns out that this model was introduced forty years ago using intrinsically probabilistic methods. In this talk I will explain how delicate probabilistic problems associated with Brownian motion in cones can be solved using functional equations, in particular Galois results on the nature of the solutions to such equations. This talk is based on work with several co-authors, mainly arXiv:2101.01562 and arXiv:2401.10734.

Thursday, July 4, 2024

Matteo Mucciconi (University of Warwick)

Time: 2.05 pm, Thursday, July 4, 2024

Location: JCMB 5323

Zoom link:  https://ed-ac-uk.zoom.us/j/81912013907

Meeting ID:  819 1201 3907

Passcode: nbps2023

Title: Large Deviations for the height function of the deformed polynuclear growth.
Abstract:
The deformed polynuclear growth is a growth process that generalizes the polynuclear growth studied in the context of KPZ universality class. In this talk, I will discuss the mathematical derivation of large time large deviations for the height function. Rare events, as functions of the time t, display distinct decay rates based on whether the height function grows significantly larger (upper tail) or smaller (lower tail) than the expected value. Upper tails exhibit an exponential decay with rate function which we determine explicitly. Conversely, the lower tails experience a more rapid decay and the rate function is given in terms of a variational problem.
Our analysis relies on two inputs. The first is a connection between the height function hand an important measure on the set of integer partitions, the Poissonized Plancherel measure, which stems from nontrivial applications of the celebrated Robinson-Schensted-Knuth correspondence. The second ingredient is the derivation of a priori convexity bounds for the rate function, which combines combinatorial and probabilistic arguments.
This is a joint work with S.Das (Chicago) and Y.Liao (Wisconsin-Madison).
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