A combinatorial and probabilistic study of initial and end heights of descents in samples of geometrically distributed random variables and in permutationsReportar como inadecuado




A combinatorial and probabilistic study of initial and end heights of descents in samples of geometrically distributed random variables and in permutations - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

1 ULB - Département d-Informatique Bruxelles 2 DMS - Department of Mathematical Sciences Matieland, Stellenbosch Uni.

Abstract : In words, generated by independent geometrically distributed random variables, we study the lth descent, which is, roughly speaking, the lth occurrence of a neighbouring pair ab with a>b. The value a is called the initial height, and b the end height. We study these two random variables and some similar ones by combinatorial and probabilistic tools. We find in all instances a generating function Ψv,u, where the coefficient of vjui refers to the jth descent ascent, and i to the initial end height. From this, various conclusions can be drawn, in particular expected values. In the probabilistic part, a Markov chain model is used, which allows to get explicit expressions for the heights of the second descent. In principle, one could go further, but the complexity of the results forbids it. This is extended to permutations of a large number of elements. Methods from q-analysis are used to simplify the expressions. This is the reason that we confine ourselves to the geometric distribution only. For general discrete distributions, no such tools are available.





Autor: Guy Louchard - Helmut Prodinger -

Fuente: https://hal.archives-ouvertes.fr/



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