We study a branching-annihilating random walk in which particles evolve on the lattice in discrete generations. Each particle produces a Poissonian number of offspring which independently move to a uniformly chosen site within a fixed distance from their parent's position. Whenever a site is occupied by at least two particles, all the particles at that site are annihilated. This models a...
Stochastic reaction networks (SRNs) are a general class of continuous-time Markov jump processes used to model a wide range of systems, including biochemical dynamics in single cells, ecological and epidemiological populations, and queueing or communication networks. Yet analyzing their dynamics remains challenging because these processes are high-dimensional and their transient behavior can...
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the abundances of all considered species evolve over time. A possible approach to address this issue is to develop tools to compare the model under study with...
Every population consists of individuals who vary in their traits, and each trait may, or may not, be associated with frailty or fitness. Variation in frailty and fitness traits makes population studies prone to selective depletion bias (SDB). The issue is widespread across fields. When an ageing cohort exhibits declining mortality, is it individuals becoming healthier or selective depletion...
Traditional models of interacting particle systems often assume a fixed network of connections, which simplifies analysis but fails to capture the dynamics of many real-world phenomena. Consequently, co-evolutionary network models, where the network structure and particle states evolve in mutual influence, are increasingly recognised as essential in diverse fields. For instance, in...
The contact process, or SIS epidemic, is a continuous-time Markov process used to model the spread of infection on a graph. Each vertex is either healthy or infected, and each infected vertex independently infects each of its healthy neighbors at rate $\lambda$ and recovers at rate $1$. We study the contact process in the presence of additional intervention measures by introducing a third...
Self-intersection local times of a random process are random variables describing how much time the process spends in small neighbourhoods of points where the trajectory intersects itself a multiple number of times. Le Gallโs classical result on the asymptotic expansion of the planar Wiener sausage (1990) shows that self-intersection local times are geometric characteristics of random...
Biological information processing is constrained by energetic costs, making it natural to treat information flow and dissipation jointly. We develop a unified framework for continuous-time chemical reaction networks (CRNs) that couples trajectory-level mutual and directed information between disjoint species sets with process-based stochastic thermodynamics for open, multi-reservoir systems....
Biology has been often touted as the new physics for mathematics with the promise of new theorems that are inspired by biological investigations. The proposed mini-symposium will discuss new theoretical results and open problems in probability theory and stochastic processes, which are inspired by models in biology. In particular, the session will provide an overview of stochastic models...
