2021
DOI: 10.48550/arxiv.2112.03567
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Lattice walks confined to an octant in dimension 3: (non-)rationality of the second critical exponent

Abstract: In the field of enumeration of walks in cones, it is known how to compute asymptotically the number of excursions (finite paths in the cone with fixed length, starting and ending points, using jumps from a given step set). As it turns out, the associated critical exponent is related to the eigenvalues of a certain Dirichlet problem on a spherical domain. An important underlying question is to decide whether this asymptotic exponent is a (non-)rational number, as this has important consequences on the algebraic… Show more

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