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Abstract We consider the large deviations from the hydrodynamic limit of the Totally Asymmetric Simple Exclusion Process (TASEP). This problem was studied by Jensen and Varadhan and was shown to be related to entropy production in the inviscid Burgers equation. Here we prove the full large deviation principle. Our method relies on the explicit formula of Matetski, Quastel, and Remenik for the transition probabilities of the TASEP.
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Large deviations for subcomplex counts and Betti numbers in multiparameter simplicial complexes
We consider the multiparameter random simplicial complex as a higher dimensional extension of the classical Erdős–Rényi graph. We investigate appearance of “unusual” topological structures in the complex from the point of view of large deviations. We first study upper tail large deviation probabilities for subcomplex counts, deriving the order of magnitude of such probabilities at the logarithmic scale precision. The obtained results are then applied to analyze large deviations for the number of simplices of the multiparameter simplicial complexes. Finally, these results are also used to deduce large deviation estimates for Betti numbers of the complex in the critical dimension.
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- Award ID(s):
- 2015242
- PAR ID:
- 10418818
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Random Structures & Algorithms
- Volume:
- 63
- Issue:
- 2
- ISSN:
- 1042-9832
- Page Range / eLocation ID:
- p. 533-556
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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