4 papers · 2 filters
The Hydrodynamic Limit of Hawkes Processes on Adaptive Stochastic Networks
James MacLaurin
We determine the large size limit of a network of interacting Hawkes Processes on an adaptive network. The flipping of the node variables is taken to have an intensity given by the…
Large Deviations of Mean-Field Jump-Markov Processes on Structured Sparse Disordered Graphs
James MacLaurin
We prove a Large Deviation Principle for {\color{blue} jump-Markov } Processes on sparse large disordered network with disordered connectivity. The network is embedded in a geometr…
Neural Fields and Noise-Induced Patterns in Neurons on Large Disordered Networks
Daniele Avitabile, James MacLaurin
We study pattern formation in class of a large-dimensional neural networks posed on random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions on cou…
Large Deviations of Piecewise-Deterministic-Markov-Processes with Application to Stochastic Calcium Waves
Gaetan Barbet, James MacLaurin, Moshe Silverstein
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 limi…