School of Mathematical Sciences

The local equation for locally interacting SDEs

Date(s)
Thursday 9th May 2024 (14:00-15:00)
Contact
Event Convenor Contact: Riccardo.Corradin@nottingham.ac.uk

Description
Speaker's Name: William Salkeld
Speaker's Affiliation: University of Nottingham
Speaker's Research Theme(s): Statistics and Probability,
Abstract:
In this talk, I will discuss the dynamics of a collection of Gaussian stochastic differential equations indexed by a locally finite graph. The drift of each individual equation is dependent only on the dynamics of the individual and their neighbourhood so that each equation exhibits correlation with a small number of other equations via these local interactions. Such local interactions arise in statistical physics and engineering and are suitable for applications when long range interactions between distant individuals are described via a sequence of local interactions between neighbours. The price we pay for considering local interactions instead of macroscopic ‘mean-field’ interactions is that the when the number of equations is large we do not expect the statistical decoupling of any pair of equations. Instead, the dynamics exhibit a ‘Markov Random Field’ property where equations are conditionally independent of one another conditioning on an appropriate separating subset. Further, these systems of equations are continuously dependent on the underlying graph structure so that changes in the interactions leads to proportional changes in the all equations. These fundamental properties of the entire system of equations is key to understanding the microscopic dynamics of each individual equation, their neighbourhood and how we simulate them.

Venue: Mathematical Sciences A17

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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