Asymptotics of Selberg-like integrals by lattice path counting
نویسندگان
چکیده
منابع مشابه
Talmudic Lattice Path Counting
Consider all planar walks, with positive unit steps (1, 0) and (0, 1), from the origin (0, 0) to a given point (a, b). Let L be the line joining the beginning to the end, i.e., the line b x a y = 0. Call the region below L "downtown," and the region above L "uptown," the line L being the border-line between downtown and uptown. Each such walk has a + b 1 points, not counting the endpoints. For ...
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Abstract. A formula for counting lattice paths in the plane from μ = (μ1, μ2) to λ = (λ1, λ2) which do not cross the lines y = x + d and y = x + c, where c, d ∈ Z and d > c, by descents and major index is given. The proof, which is purely combinatorial, uses a bijection on certain two–rowed tableaux. As application, formulas for the joint distribution of Kolmogorov–Smirnov and run statistics ar...
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ژورنال
عنوان ژورنال: Annals of Physics
سال: 2011
ISSN: 0003-4916
DOI: 10.1016/j.aop.2010.09.007