Macroscopic equations arising out of stochastic particle systems in detailed balance (called
dissipative systems or gradient flows) have a natural variational structure, which can be …

We consider the thermodynamic limit of mean-field stochastic particle systems on a
complete graph. The evolution of occupation number at each vertex is driven by particle …

Chemical reactions can be modeled by a random time-changed Poisson process on
countable states. The macroscopic behaviors, such as large fluctuations, can be studied via …

Chemical reactions can be modeled by a random time-changed Poisson process on
countable states. The macroscopic behaviors such as the large fluctuations can be studied …

In a stochastic reaction network setting we consider the problem of tracking the fate of
individual molecules. We show that by using the classical large volume limit results, we may …

We prove a Large Deviation Principle for Piecewise Deterministic Markov Processes
(PDMPs). This is an asymptotic estimate for the probability of a trajectory in the large size …

Recent developments in Macroscopic Fluctuation Theory show that many interacting particle
systems behave macroscopically as a combination of a gradient flow with Hamiltonian …

We prove a Large Deviation Principle for Hawkes Processes on sparse large disordered
networks with a graphon structure. We apply our results to a stochastic SIS epidemiological …

We study a spatial Markovian particle system with pairwise coagulation, a spatial version of
the Marcus--Lushnikov process: according to a coagulation kernel $ K $, particle pairs …

We study a micro and macroscopic model for chemical reactions with feedback between
reactions and temperature of the solute. The first result concerns the quasipotential as the …