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Journal Articles ALEA : Latin American Journal of Probability and Mathematical Statistics Year : 2019

Longest increasing paths with gaps


We consider a variant of the continuous and discrete Ulam-Hammersley problems: we study the maximal length of an increasing path through a Poisson point process (or a Bernoulli point process) with the restriction that there must be minimal gaps between abscissae and ordinates of successive points of the path. For both cases (continuous and discrete) our approach rely on couplings with well-studied models: respectively the classical Ulam-Hammersley problem and last-passage percolation with geometric weights. Thanks to these couplings we obtain explicit limiting shapes in both settings. We also establish that, as in the classical Ulam-Hammersley problem, the fluctuations around the mean are given by the Tracy-Widom distribution.
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hal-01796897 , version 1 (22-05-2018)
hal-01796897 , version 2 (25-02-2019)



Anne-Laure Basdevant, Lucas Gerin. Longest increasing paths with gaps. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2019, 16 (2), pp.1141--1163. ⟨hal-01796897v2⟩
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