Scaling limits of stochastic models with Fast Absorption and Slow Escape

Abstract: Autocatalytic reaction systems often exhibit a peculiar switching behaviour, due to random fluctuations and discreteness in the number of molecules, which produces the phenomenon of discreteness-induced transitions. The 2-dimensional version of a model proposed by Togashi and Kaneko (2001) is a prominent example of such patten. We analyze this model within a multiscale framework, in which fast autocatalytic cascades are triggered by much slower inflow and outflow reactions. Under suitable assumptions, we study the limit behaviour of the rescaled stochastic process, and prove weak convergence to a naturally arising piecewise-deterministic Markov process on the Skorohod space equipped with Jakubowsky S-topology. Building upon this model, we discuss extensions of such procedure to a larger family of autocatalytic reaction systems, in which a fast subsystem is rapidly absorbed into a set of absorbing states, occasionally giving rise to abrupt state switches of possibly random size.

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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