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Random sampling of lattice paths with constraints, via transportation

Abstract : We build and analyze in this paper Markov chains for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. These chains are easy to implement, and sample an "almost" uniform path of length $n$ in $n^{3+\epsilon}$ steps. This bound makes use of a certain $\textit{contraction property}$ of the Markov chain, and is proved with an approach inspired by optimal transport.
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Lucas Gerin. Random sampling of lattice paths with constraints, via transportation. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. pp.317-328, ⟨10.46298/dmtcs.2783⟩. ⟨hal-00439479v4⟩

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