North-East and Midlands Stochastic Analysis Seminars
NEMSA
The Northeast-Midlands Stochastic Analysis Seminar (NEMSA) is a seminar series jointly organised by the Universities of Durham, Oxford, Warwick and York. The seminars normally take place four times a year, rotating between the four organising institutions.
In 2024, the Warwick leg of NEMSA will be held on 17 September 2024 at the University of Warwick. In this meeting we will be joining forces with the closely related Dualities in Probability and Algebra
workshop in Lancaster on 16 and 17 September. The current plan is that the attendees to the Lancaster workshop will be able to watch all of the talks below via a Livestream in Lancaster in the afternoon of 17 September (Penington's talk will be online in any case).The workshop is kindly supported by the CRISM Centre at the University of Warwick, the Isaac Newton Institute Network grant and the London Mathematical Society Network grant.
Confirmed Speakers in Warwick
Sarah Penington (Bath, online)
Dario Spanò (Warwick)
Frank Redig (TU Delft)
Speakers for Dualities in Probability and Algebra in Lancaster
See website.
Organising Committee:
Horatio Boedihardjo (Warwick Statistics), Zdzislaw Brzezniak (York), Paul Chleboun (Warwick Statistics), David Elworthy (Warwick Maths), Chunrong Feng (Durham), Massimiliano Gubinelli (Oxford), Roger Tribe (Warwick Maths), Zhongmin Qian (Oxford), Daniel Valesin (Warwick Statistics) and Huaizhong Zhao (Durham).
Contact: horatio.boedihardjo@warwick.ac.uk
Attendance and Registration
Please register at the link below so that we have an idea of numbers for catering.
Location
All talks take place in Zeeman Building room MS.05 at the University of Warwick.
Information on travelling to the university can be found here. In particular, the best train station is Coventry, to which there are direct trains from Birmingham (around 20 minutes) and London Euston (around 1 hour). The closest airport is Birmingham International, though London airports have more availability for longer flights.
Schedule
Tuesday 17th September
12:15-13:15 Lunch
13:30-14:30 Sarah Penington (online)
14:30-15:30 Dario Spano
15:30-16:00 Coffee Break
16:00-17:00 Frank Redig
Evening Dinner
Title and Abstract
Sarah Penington
Dario Spano
Title: Dualities and intertwinings in population genetics diffusions and beyond.
Abstract: Mathematical population genetics has been an incredible culture broth for the recent developments of the modern theory of stochastic duality. Duality in genetics clarifies the intrinsic link between forward-in-time dynamics of a population’s allele frequencies evolution and backward-in-time dynamics of the same population’s ancestry. It has yielded a probabilistic insight into the spectral properties of both processes, helping significantly the tractability of such processes for simulation and inference. I will review some aspects of stochastic duality - and related intertwining operators - playing a key role in the analysis of Wright-Fisher diffusion processes of population genetics and in some of their generalisations, for which some open problems will be discussed.
Frank Redig
Title: Intertwining and mixed product states
Abstract:
We will discuss duality and intertwining properties of mass transport models.
More precisely, we will discuss mass transport models of non-equilibrium such as the KMP model, and the recently introduced ``harmonic model’’.
We show that their non-equilibrium steady state is a mixture of product measures, where the probability measure which describes the mixture is in turn the stationary distribution of an intertwined process, the so-called hidden parameter model. For the harmonic model we show that the hidden parameter model has an additional spatial Markov property, which in the case of a chain geometry. leads naturally to an explicit formula for the stationary state, previously obtained with other (among which integrability) techniques.
Based on joint work with C. Giardina and B. van Tol
References
- Giardinà, C., Redig, F., & van Tol, B. (2024).Intertwining and propagation of mixtures for generalized KMP models and harmonic models.arXiv preprint arXiv:2406.01160.
- Carinci, G., Franceschini, C., Frassek, R., Giardinà, C., & Redig, F. (2023). The open harmonic process: non-equilibrium steady state, pressure, density large deviation and additivity principle.arXiv preprint arXiv:2307.14975.
- Carinci, G., Franceschini, C., Gabrielli, D., Giardinà, C., & Tsagkarogiannis, D. (2024).Solvable stationary non equilibrium states.Journal of Statistical Physics,191(1), 10.