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Competing first pas...
Competing first passage percolation on random graphs with finite variance degrees
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- Ahlberg, Daniel (författare)
- Stockholms universitet,Matematiska institutionen,Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden
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- Deijfen, Maria (författare)
- Stockholms universitet,Matematiska institutionen,Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden
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- Janson, Svante, 1955- (författare)
- Uppsala universitet,Analys och sannolikhetsteori
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(creator_code:org_t)
- 2019-03-05
- 2019
- Engelska.
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Ingår i: Random structures & algorithms (Print). - : Wiley. - 1042-9832 .- 1098-2418. ; 55:3, s. 545-559
- Relaterad länk:
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http://arxiv.org/pdf...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph in that an uninfected vertex becomes type 1 (2) infected at rate lambda(1) (lambda(2)) times the number of nearest neighbors of type 1 (2). Assuming (essentially) that the degree of a randomly chosen vertex has finite second moment, we show that if lambda(1) = lambda(2), then the fraction of vertices that are ultimately infected by type 1 converges to a continuous random variable V is an element of (0,1), as the number of vertices tends to infinity. Both infection types hence occupy a positive (random) fraction of the vertices. If lambda(1) not equal lambda(2), on the other hand, then the type with the larger intensity occupies all but a vanishing fraction of the vertices. Our results apply also to a uniformly chosen simple graph with the given degree sequence.
Ämnesord
- NATURVETENSKAP -- Data- och informationsvetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- coexistence
- competing growth
- configuration model
- continuous-time branching process
- first passage percolation
- random graphs
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- ref (ämneskategori)
- art (ämneskategori)
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