Large Deviations for Degenerate Markov Jump Processes

Abstract: The dynamics of a network of chemical reactions under the laws of mass action kinetics are typically modeled as a system of coupled ordinary differential equations. This macroscopic model can be recovered, under the appropriate scaling, as the functional law of large numbers for a family of jump Markov processes capturing the discrete nature of the underlying, microscopic dynamical model. The large deviations behavior of these models has been recently investigated under relatively strong assumptions on the existence of reactions with rates bounded away from 0, allowing to guarantee the nondegeneracy of the Markov process being investigated. We show that these assumptions, which are violated by many models of interest, can be significantly relaxed, establishing large deviations principles for a large class of degenerate jump Markov processes.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

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This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom!

The organizers.

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