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Applied Probability Seminars

This is an informal seminar to to give academic staff and graduate students, based or hosted in Warwick (any department), the opportunity to know more about each other’s research on topics of probability and its uses in related areas such as mathematical statistics, statistical physics, computer sciences, analysis, et cetera.

PhD students and postdocs are particularly encouraged to contribute, as well as any external speaker from another Department or University that you would like to invite. Please contact Dario Spanò (d.spano<at>warwick.ac.uk) if you wish to give a talk or if you have a name of speaker to suggest.

Below is a provisional schedule of the upcoming talks. GIven the informal nature of the seminar, last minnute changes may happen. Please join the Applied probability Seminar Teams channel to receive up to date information.

Academic Year 2021-22, Term 3

Venue: MB0.08 or Online (Teams link will be provided below each abstract)

Time: 11:00 unless otherwise stated

6 May 2022

Speaker: Horatio Boedihardjo

Title: Do solutions to hypoelliptic differential equations with bounded vector fields driven by Gaussian processes necessarily have Gaussian tails?

Abstract

Given a stochastic process X, what can we say about the probability distribution for the solution to differential equation driven by X? One way to study this question is to see if the solution has a density function and if so what properties do the density function have. These questions are well-studied classically when X is a Brownian motion, when the differential equation are defined in the sense of Ito. Rough path theory has enabled us to make sense of differential equation driven by more general Gaussian processes (and beyond), with much recent progress in understanding the distribution of the solution in this extended setting. We will explore one of these questions, namely whether the solution necessarily has a Gaussian tail? The answer is yes for fractional Brownian motion with Hurst parameter H=>1/2, but we will report some preliminary findings about a different behaviour when H<1/2. Joint work, in progress, with Xi Geng.
 
 
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13 May 2022

Speaker: Leonardo Rolla

Title: Local and global behaviour of the subcritical contact process

Abstract: We will describe the scaling limit of the subcritical contact process in terms of a marked Poisson point process and a quasi-stationary distribution, and discuss the question of uniqueness of the QSD in this and other contexts. Based on joint works with E. Andjel, F. Ezanno and P. Groisman, with Aurelia Deshayes, and with F. Arrejoría and P. Groisman.

Teams link

 

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20 May 2022

Speaker: Oleg Zaboronsky

Title: On the origin of Markov dualities for interacting particle systems on Z

Abstract:

As it turns out, several classes of interacting particle systems on Z (annihilating-coalescing random walks, annihilating random walks with immigration, branching coalescing random walks) are exactly solvable for any deterministic initial conditions. In particular, the fixed time distribution of particles turns out to be a Pfaffian point process, which allows one to study interesting statistics of the system, such as gap probabilities. The exact solvability is due to a family of Markov dualities relating each of the listed models to annihilating random walks with finitely many initial particles. Is there an underlying reason behind the existence of duality for all these systems? In the talk, I will show how to construct the dualities by studying representations of the algebra of two-site model generators, observe the appearance of Hecke algebra and explain its significance. No knowledge of algebra beyond linear algebra will be assumed. (Based on work in progress jointly with Tribe, Westbury, Povolotskiy, Pyatov)

 

 

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27 May 2022

Speaker: Daniel Valesin

Title: TBC

Abstract: TBC

 

 

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3 June 2022: Bank Holiday

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10 June 2022:

Speaker: Juan Kuntz

Title: TBC

Abstract: TBC

 

 

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17 June 2022

Speaker: TBA

Title: TBC

Abstract: TBC

 

 

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24 June 2022

Speaker: Ivana Valentic

Title: TBC

Abstract: TBC

 

 

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1 July 2022

Speaker: GIuseppe Cannizzaro

Title: TBC

Abstract: TBC