Some large deviations in Kingman's coalescent
Depperschmidt A, Pfaffelhuber P, Scheuringer A (2015)
Publication Type: Journal article, Original article
Publication year: 2015
Journal
Book Volume: 20
Pages Range: 1-14
DOI: 10.1214/ECP.v20-3107
Abstract
Kingman's coalescent is a random tree that arises from classical population genetic models such as the Moran model. Concerning the structure of the tree-top there are two well-known laws of large numbers: (i) The (shortest) distance, denoted by Tn, from the tree-top to the level when there are n lines in the tree satisfies almost surely; (ii) At time Tn, the population is naturally partitioned in exactly n families where individuals belong to the same family if they have a common ancestor at time Tn in the past. If denotes the relative size of the ith family, then almost surely. For both laws of large numbers we prove corresponding large deviations results. For (i), the rate of the large deviations is n and we can give the rate function explicitly. For (ii), the rate is n for downwards deviations and √n for upwards deviations. In both cases we give exact rate functions.
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APA:
Depperschmidt, A., Pfaffelhuber, P., & Scheuringer, A. (2015). Some large deviations in Kingman's coalescent. Electronic Communications in Probability, 20, 1-14. https://dx.doi.org/10.1214/ECP.v20-3107
MLA:
Depperschmidt, Andrej, Peter Pfaffelhuber, and Annika Scheuringer. "Some large deviations in Kingman's coalescent." Electronic Communications in Probability 20 (2015): 1-14.
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