Lengths and heights of random walk excursions
Consider a simple symmetric random walk on the line. The parts of the random walk between consecutive returns to the origin are called excursions. The heights and lengths of these excursions can be arranged in decreasing order. In this paper we give the exact and limiting distributions of these rank...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2003-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3337/pdf |
| _version_ | 1827324173553238016 |
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| author | Endre Csáki Yueyun Hu |
| author_facet | Endre Csáki Yueyun Hu |
| author_sort | Endre Csáki |
| collection | DOAJ |
| description | Consider a simple symmetric random walk on the line. The parts of the random walk between consecutive returns to the origin are called excursions. The heights and lengths of these excursions can be arranged in decreasing order. In this paper we give the exact and limiting distributions of these ranked quantities. These results are analogues of the corresponding results of Pitman and Yor [1997, 1998, 2001] for Brownian motion. |
| first_indexed | 2024-04-25T02:07:51Z |
| format | Article |
| id | doaj.art-f364174e7df44e94a584b4a9b641026b |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:07:51Z |
| publishDate | 2003-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-f364174e7df44e94a584b4a9b641026b2024-03-07T14:29:56ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502003-01-01DMTCS Proceedings vol. AC,...Proceedings10.46298/dmtcs.33373337Lengths and heights of random walk excursionsEndre Csáki0Yueyun Hu1Alfréd Rényi Institute of MathematicsLaboratoire de Probabilités et Modèles AléatoiresConsider a simple symmetric random walk on the line. The parts of the random walk between consecutive returns to the origin are called excursions. The heights and lengths of these excursions can be arranged in decreasing order. In this paper we give the exact and limiting distributions of these ranked quantities. These results are analogues of the corresponding results of Pitman and Yor [1997, 1998, 2001] for Brownian motion.https://dmtcs.episciences.org/3337/pdfsimple random walkexcursion lengthexcursion height[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds][info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co][info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| spellingShingle | Endre Csáki Yueyun Hu Lengths and heights of random walk excursions Discrete Mathematics & Theoretical Computer Science simple random walk excursion length excursion height [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| title | Lengths and heights of random walk excursions |
| title_full | Lengths and heights of random walk excursions |
| title_fullStr | Lengths and heights of random walk excursions |
| title_full_unstemmed | Lengths and heights of random walk excursions |
| title_short | Lengths and heights of random walk excursions |
| title_sort | lengths and heights of random walk excursions |
| topic | simple random walk excursion length excursion height [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| url | https://dmtcs.episciences.org/3337/pdf |
| work_keys_str_mv | AT endrecsaki lengthsandheightsofrandomwalkexcursions AT yueyunhu lengthsandheightsofrandomwalkexcursions |