Lattice paths with catastrophes

In queuing theory, it is usual to have some models with a "reset" of the queue. In terms of lattice paths, it is like having the possibility of jumping from any altitude to zero. These objects have the interesting feature that they do not have the same intuitive probabilistic behaviour as...

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Vydáno v:Discrete mathematics and theoretical computer science Ročník 19 no. 1; číslo Analysis of Algorithms; s. 1 - 32
Hlavní autoři: Banderier, Cyril, Wallner, Michael
Médium: Journal Article
Jazyk:angličtina
Vydáno: Nancy DMTCS 01.01.2017
Discrete Mathematics & Theoretical Computer Science
Témata:
05a16, 05a19, 60f05
Brownian motion
Combinatorial analysis
Combinatorics
Complex Variables
Computer Science
computer science - discrete mathematics
Data Structures and Algorithms
Discrete Mathematics
Encyclopedias
Enumeration
Formal Languages and Automata Theory
Jumping
Mathematics
mathematics - combinatorics
mathematics - probability
Probability
Queues
Queuing theory
Symbolic Computation
ISSN:1365-8050, 1462-7264, 1365-8050
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Shrnutí:In queuing theory, it is usual to have some models with a "reset" of the queue. In terms of lattice paths, it is like having the possibility of jumping from any altitude to zero. These objects have the interesting feature that they do not have the same intuitive probabilistic behaviour as classical Dyck paths (the typical properties of which are strongly related to Brownian motion theory), and this article quantifies some relations between these two types of paths. We give a bijection with some other lattice paths and a link with a continued fraction expansion. Furthermore, we prove several formulae for related combinatorial structures conjectured in the On-Line Encyclopedia of Integer Sequences. Thanks to the kernel method and via analytic combinatorics, we provide the enumeration and limit laws of these "lattice paths with catastrophes" for any finite set of jumps. We end with an algorithm to generate such lattice paths uniformly at random. Comment: 32 pages
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.23638/DMTCS-19-1-23