We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Markov processes on quasi-random graphs.
- Authors
Keliger, D.
- Abstract
We study Markov population processes on large graphs, with the local state transition rates of a single vertex being a linear function of its neighborhood. A simple way to approximate such processes is by a system of ODEs called the homogeneous mean-field approximation (HMFA). Our main result is showing that HMFA is guaranteed to be the large graph limit of the stochastic dynamics on a finite time horizon if and only if the graph-sequence is quasi-random. An explicit error bound is given and it is 1 N plus the largest discrepancy of the graph. For Erdős–Rényi and random regular graphs we show an error bound of order the inverse square root of the average degree. In general, diverging average degrees is shown to be a necessary condition for the HMFA to be accurate. Under special conditions, some of these results also apply to more detailed type of approximations like the inhomogenous mean field approximation (IHMFA). We pay special attention to epidemic applications such as the SIS process.
- Subjects
MARKOV processes; RANDOM graphs; REGULAR graphs; TIME perspective; SQUARE root
- Publication
Acta Mathematica Hungarica, 2024, Vol 173, Issue 1, p20
- ISSN
0236-5294
- Publication type
Academic Journal
- DOI
10.1007/s10474-024-01441-y