منابع مشابه
Random Walks and Random Permutations
A connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences. Consequently the scaled distribution of the maximum displacements in a particular asymmeteric version of the model can be determined to be the same as the scaled distribution of the eigenvalues at the soft edge of the GUE. The scaling of the distribution gives...
متن کاملSymmetrized random permutations
Selecting N random points in a unit square corresponds to selecting a random permutation. Placing symmetry restrictions on the points, we obtain special kinds of permutations : involutions, signed permutations and signed involutions. We are interested in the statistics of the length (in numbers of points) of the longest up/right path in each symmetry type as the number of points increases to in...
متن کاملRandom Maps and Permutations
Proof Write Ck as the sum of indicator random variables 1γ , for γ a k-cycle. This means that 1γ(π) is 1 if γ is a cycle of π and 0 otherwise. Then E(Ck) = ∑ γ E(1γ). To determine E(1γ) we count the number of permutations having γ as a cycle. That number is (n− k)!. Thus, E(1γ) = (n − k)!/n!. Now, the number of possible γ is n(n − 1) · · · (n − k + 1)/k, since a k-cycle is an ordered selection ...
متن کاملVerifiable Random Permutations
Pseudorandom Functions (PRFs), introduced by Goldreich, Goldwasser and Micali [9], allow one to efficiently simulate the computation of a function which is indistinguishable from a truly random function. A seemingly stronger primitive is that of a (strong) pseudorandom permutation (PRP) [13], which allows one to efficiently simulate a truly random permutation (and its inverse). The celebrated r...
متن کاملDescending subsequences of random permutations
Given a random permutation of the numbers 1, 2, . . . . n, let L, be the length of the longest descending subsequence of this permutation. Let F, be the minimal header (first element) of the descending subsequences having maximal length. It is known that EL,/&,,,, c and that c=2. However, the proofs that r=2 are far from elementary and involve limit processes. Several relationships between thes...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2020
ISSN: 0024-6093,1469-2120
DOI: 10.1112/blms.12345