Layering of the Poisson process in the quadrant

• Autorzy: Levikson B. , Rolski T. , Weiss G.
• Języki publikacji: EN

Abstrakty

EN

We consider the increasing sequence of non-intersecting monotone decreasing step processes Y*_n(t), n = 1, 2,...(t > 0), whose jump points cover all the points of the homogeneous rate 1 Poisson process on the quadrant R²₊. We deriveproperties of these processes, in particular the marginal distributions P(Y*_n(t) > x), in terms of a Toeplitz determinant of some modified Bessel functions. Our system provides a new view of the Hammersley interacting particle system discussed by Aldousand Diaconis, and the distributions we derive are related tothe distribution of the length of the longest ascending sequence in a random permutation.

Słowa kluczowe

EN

Planar Poisson process; kth layer process; modified Bessel function; Hammersley interacting particle system; longest increasing subsequence; Ulam problem; random permutation

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 2
• Strony: 417--440
• Opis fizyczny: Bibliogr.14 poz., wykr.

Twórcy

autor

Levikson B.

• Department of Statistics, Haifa University, Israel

autor

Rolski T.

• Institute of Mathematics, Wroclaw University, Poland

autor

Weiss G.

• Department of Statistics, Haifa University, Israel

Bibliografia

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