Celebratio Mathematica — Liggett — Complete Bibliography

Complete Bibliography

Works connected to Rinaldo Bruno Schinazi

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T. M. Liggett, R. B. Schinazi, and J. Schweinsberg: “A contact process with mutations on a tree,” Stochastic Process. Appl. 118 : 3 (2008), pp. 319–332. MR 2389047 Zbl 1141.60065 ArXiv math/0612564 article

Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate \( \lambda \). When a new pathogen is born, it has the same type as its parent with probability \( 1-r \). With probability \( r \), a mutation occurs, and the new pathogen has a different type from all previously observed pathogens. When a new type appears in the population, it survives for an exponential amount of time with mean 1, independently of all the other types. All pathogens of that type are killed simultaneously. Schinazi and Schweinsberg [R.B. Schinazi, J. Schweinsberg, Spatial and non-spatial stochastic models for immune response, Markov Process. Related Fields (2006) (in press)] have shown that this model on \( \mathbb{Z}^d \) behaves rather differently from its non-spatial version. In this paper, we show that this model on a homogeneous tree captures features from both the non-spatial version and the version. We also obtain comparison results, between this model and the basic contact process on general graphs.

Jason Ross Schweinsberg	Related
Rinaldo Bruno Schinazi	Related

T. M. Liggett and R. B. Schinazi: “A stochastic model for phylogenetic trees,” J. Appl. Probab. 46 : 2 (June 2009), pp. 601–607. MR 2535836 Zbl 1180.60079 article