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Random Walks in Octants , and Related Structures
| Content Provider | Semantic Scholar |
|---|---|
| Author | Niederhausen, Heinrich |
| Copyright Year | 2005 |
| Abstract | A di¤usion walk in Z2 is a (random) walk with unit step vectors !, ", , and #. Particles from di¤erent sources with opposite charges cancel each other when they meet in the lattice. This cancellation principle is applied to enumerate di¤usion walks in shifted half-planes, quadrants, and octants (a 3-D version is also considered). Summing over time we calculate expected numbers of visits and rst passage probabilities. Comparing those quantities to analytically obtained expressions leads to interesting identities, many of them involving integrals over products of Chebyshev polynomials of the rst and second kind. We also explore what the expected number of visits means when the di¤usion in an octant is bijectively mapped onto other combinatorial structures, like pairs of non-intersecting Dyck paths, vicious walkers, bicolored Motzkin paths, staircase polygons in the second octant, and f!"g-paths con ned to the third hexadecant enumerated by left turns. Keywords: Random walks, lattice path enumeration, rst passage. AMS subject classi cation: Primary 60J15, Secondary 05A15, 05A19 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://math.fau.edu/Niederhausen/HTML/Papers/PlanarWalksInOctants.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Cations Chebyshev polynomials Dyck language Enumerated type Method of conditional probabilities Naruto Shippuden: Clash of Ninja Revolution 3 Neoplasm Metastasis Polynomial Probability Quantity Sense of identity (observable entity) VHDL-AMS Walkers |
| Content Type | Text |
| Resource Type | Article |
