Optimality regions and fluctuations for Bernoulli last passage models

Georgiou, Nicos and Ortmann, Janosch (2018) Optimality regions and fluctuations for Bernoulli last passage models. Mathematical Physics, Analysis and Geometry, 21 (22). pp. 1-29. ISSN 1385-0172

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Abstract

We study the sequence alignment problem and its independent version,the discrete Hammersley process with an exploration penalty.

We obtain rigorous upper bounds for the number of optimality regions in both models near the soft edge.At zero penalty the independent model becomes an exactly solvable model and we identify cases for which the law of the last passage time converges to a Tracy-Widom law.

Item Type: Article
Keywords: Soft edge, Edge results, Optimality regions, Sequence alignment, Discrete Hammersley process, Longest common subsequence, Bernoulli increasing paths, Tracy-Widom distribution, Last passage time, Corner growth models, Flat edge
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics > QA0274 Stochastic processes
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Depositing User: Nicos Georgiou
Date Deposited: 03 Aug 2018 14:25
Last Modified: 03 Aug 2018 14:25
URI: http://sro.sussex.ac.uk/id/eprint/77529

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Project NameSussex Project NumberFunderFunder Ref
The flat edge in last passage percolationG2031EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCILEP/P021409/1