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Foss S, Konstantopoulos T, Pyatkin A. Probabilistic and analytical properties of the last passage percolation constant in a weighted random directed graph. ANN APPL PROBAB 2023. [DOI: 10.1214/22-aap1832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/30/2023]
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Foss S, Konstantopoulos T, Mallein B, Ramassamy S. Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation. LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS 2023. [DOI: 10.30757/alea.v20-19] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/31/2023]
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Mallein B, Ramassamy S. Barak–Erdős graphs and the infinite-bin model. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2021. [DOI: 10.1214/20-aihp1141] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Bastien Mallein
- Université Sorbonne Paris Nord, LAGA, UMR 7539, F-93430, Villetaneuse, France
| | - Sanjay Ramassamy
- CEA Saclay, Instityt de Physique Théorique, CNRS, F-91191 Gif-sur-Yvette, France
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Mallein B, Ramassamy S. Two-sided infinite-bin models and analyticity for Barak–Erdős graphs. BERNOULLI 2019. [DOI: 10.3150/18-bej1097] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Abstract
Abstract
We consider a directed graph on the integers with a directed edge from vertex i to j present with probability n-1, whenever i < j, independently of all other edges. Moreover, to each edge (i, j) we assign weight n-1(j - i). We show that the closure of vertex 0 in such a weighted random graph converges in distribution to the Poisson-weighted infinite tree as n → ∞. In addition, we derive limit theorems for the length of the longest path in the subgraph of the Poisson-weighted infinite tree which has all vertices at weighted distance of at most ρ from the root.
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Foss S, Zachary S. Stochastic Sequences with a Regenerative Structure that May Depend Both on the Future and on the Past. ADV APPL PROBAB 2016. [DOI: 10.1239/aap/1386857859] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Many regenerative arguments in stochastic processes use random times which are akin to stopping times, but which are determined by the future as well as the past behaviour of the process of interest. Such arguments based on ‘conditioning on the future’ are usually developed in an ad-hoc way in the context of the application under consideration, thereby obscuring the underlying structure. In this paper we give a simple, unified, and more general treatment of such conditioning theory. We further give a number of novel applications to various particle system models, in particular to various flavours of contact processes and to infinite-bin models. We give a number of new results for existing and new models. We further make connections with the theory of Harris ergodicity.
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Stochastic Sequences with a Regenerative Structure that May Depend Both on the Future and on the Past. ADV APPL PROBAB 2016. [DOI: 10.1017/s0001867800006789] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
Many regenerative arguments in stochastic processes use random times which are akin to stopping times, but which are determined by the future as well as the past behaviour of the process of interest. Such arguments based on ‘conditioning on the future’ are usually developed in an ad-hoc way in the context of the application under consideration, thereby obscuring the underlying structure. In this paper we give a simple, unified, and more general treatment of such conditioning theory. We further give a number of novel applications to various particle system models, in particular to various flavours of contact processes and to infinite-bin models. We give a number of new results for existing and new models. We further make connections with the theory of Harris ergodicity.
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