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Abstract We study a stochastic compartmental susceptible–infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval. We split the population of graph vertices into two compartments, namely, S and I, denoting susceptible and infected vertices, respectively. In addition to the sizes of these two compartments, we keep track of the counts of SI-edges (those connecting a susceptible and an infected vertex) and SS-edges (those connecting two susceptible vertices). We describe the dynamical process in terms of these counts and present a functional central limit theorem (FCLT) for them as the number of vertices in the random graph grows to infinity. The FCLT asserts that the counts, when appropriately scaled, converge weakly to a continuous Gaussian vector semimartingale process in the space of vector-valued càdlàg functions endowed with the Skorokhod topology. We discuss applications of the FCLT in percolation theory and in modelling the spread of computer viruses. We also provide simulation results illustrating the FCLT for some common degree distributions.
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Localization Theorem for Homological Vector Fields
Abstract We present a general theorem which computes the cohomology of a homological vector field on global sections of vector bundles over smooth affine supervarieties. The hypotheses and results have the clear flavor of a localization theorem.
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- Award ID(s):
- 2001191
- PAR ID:
- 10490238
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Communications in Mathematical Physics
- Volume:
- 405
- Issue:
- 2
- ISSN:
- 0010-3616
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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