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Last-Passage Percolation with constraints, and applications to polymers in random environment

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Hammersley’s Last-Passage Percolation (LPP) problem can be described as follows: let m points be drawn uniformly and independently in [0,1]^2, then what is the maximal number of points that can be collected by an up-right path? In this talk, I will introduce a generalization of this problem, where the up-right condition is changed to a global condition on the path. Results on this new LPP with constraints are limited, but they already have some applications, in particular in the context of polymers in random environment. (Joint work with Niccolò Torri)

This talk is part of the Probability series.

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