Vicious walkers and hook Young tableaux
نویسندگان
چکیده
منابع مشابه
Vicious Walkers and Hook Young Tableaux
We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of walker’s movements. Applying the saddle point method, we reveal that the scaling limit gives the Tracy–Widom distribution, which is same with the limit distribution of...
متن کاملVicious walkers and Young tableaux I: without walls
We rederive previously known results for the number of star and watermelon configurations by showing that these follow immediately from standard results in the theory of Young tableaux and integer partitions. In this way we provide a proof of a result, previously only conjectured, for the total number of stars.
متن کاملVicious Walkers, Friendly Walkers, and Young Tableaux. III. Between Two Walls
1 Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Vienna, Austria. 2 Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia; e-mail: [email protected] 3 LaBRI, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France. 4 Present address: Institut Gerard Desargues, Université Claude Bernard Lyon-I, Bâtiment B...
متن کاملVicious Walkers, Friendly Walkers and Young Tableaux Ii: with a Wall
We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of Young tableaux, and combinatorial descriptions of symmetric functions. For the problem of n-friendly walkers, we derive exact asymptotics for the number of stars and watermelons both in the absen...
متن کاملLattice paths: vicious walkers and friendly walkers
In an earlier paper [4] the problem of vicious random walkers on a d-dimensional directed lattice was considered. \Vicious walkers" describes the situation in which two or more walkers arriving at the same lattice site annihilate one another. Accordingly, the only allowed con gurations are those in which contacts are forbidden. Alternatively expressed as a static rather than dynamic problem, vi...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2003
ISSN: 0305-4470
DOI: 10.1088/0305-4470/36/12/311