arXiv subjects

Daniel Keliger

Publications and source records attributed to Daniel Keliger.

3 recordsLinked to original sources

arXiv2022

Accuracy criterion for mean field approximations of Markov processes on hypergraphs

We provide error bounds for the N-intertwined mean-field approximation (NIMFA) for local density-dependent Markov population processes with a well-distributed underlying network structure showing NIMFA being accurate when a typical vertex has many neighbors. The result justifies some of the most common approximations used in epidemiology, statistical physics and opinion dynamics literature under certain conditions. We allow interactions between more than 2 individuals, and an underlying hypergraph structure accordingly.

math.PR↗

arXiv2020

Local-density dependent Markov processes on graphons with epidemiological applications

We investigate local-density dependent Markov processes on a class of large graphs sampled from a graphon, where the transition rates of the vertices are influenced by the states of their neighbors. We show that as the average degree converges to infinity, the evolution of the process in the transient regime converges to the solution of a set of non-local integro-partial differential equations. We also provide rigorous derivation for the epidemic threshold in the case of the Susceptible-Infected-Susceptible (SIS) process on such graphons.

math.PR↗

arXiv2020

Mean field limit of local density-dependent Markov processes on weighted Erdos-Renyi graphs

We study the asymptotic behaviour of Markov processes on large weighted Erdos-Renyi graphs where the transition rates of the vertices are only influenced by the state of their neighbours and the corresponding weight on the edges. We find the ratio of vertices being in a certain state will converge to the solution of a differential equation obtained from mean field approximation if the graph is dense enough, namely, the average degree is at least of order $N^{\frac{1}{2}+\epsilon}$. Proof for convergence in probability in the transient regime is shown.

math.PR↗