Spherically Symmetric Random Permutations
نویسندگان
چکیده
We consider random permutations which are spherically symmetric with respect to a metric on the symmetric group Sn and are consistent as n varies. The extreme infinitely spherically symmetric permutation-valued processes are identified for the Hamming, Kendall-tau and Caley metrics. The proofs in all three cases are based on a unified approach through stochastic monotonicity. MSC:
منابع مشابه
Spherically Symmetric Solutions in a New Braneworld Massive Gravity Theory
In this paper, a combination of the braneworld scenario and covariant de Rham-Gabadadze-Tolley (dRGT) massive Gravity theory is proposed. In this setup, the five-dimensional bulk graviton is considered to be massive. The five dimensional nonlinear ghost-free massive gravity theory affects the 3-brane dynamics and the gravitational potential on the brane. Following the solutions with spherical s...
متن کاملSpherically symmetric random walks. I. Representation in terms of orthogonal polynomials.
Spherically symmetric random walks in arbitrary dimension D can be described in terms of Gegenbauer (ultraspherical) polynomials. For example, Legendre polynomials can be used to represent the special case of two-dimensional spherically symmetric random walks. In general, there is a connection between orthogonal polynomials and semibounded one-dimensional random walks; such a random walk can be...
متن کاملAbout the Security of Ciphers (Semantic Security and Pseudo-Random Permutations)
Probabilistic symmetric encryption have already been widely studied, from a theoretical point of view. Nevertheless, many applications require length-preserving encryption, to be patched at a minimal cost to include privacy without modifying the format (e.g. encrypted filesystems). In this paper, we thus consider the security notions for length-preserving, deterministic and symmetric encryption...
متن کاملThe Probability of Generating the Symmetric Group When One of the Generators Is Random
A classical result of John Dixon (1969) asserts that a pair of random permutations of a set of n elements almost surely generates either the symmetric or the alternating group of degree n. We answer the question, “For what permutation groups G ≤ Sn do G and a random permutation σ ∈ Sn almost surely generate the symmetric or the alternating group?” Extending Dixon’s result, we prove that this is...
متن کاملSpherically symmetric random walks in noninteger dimension
A previous paper proposed a new kind of random walk on a spherically-symmetric lattice in arbitrary noninteger dimension D. Such a lattice avoids the problems associated with a hypercubic lattice in noninteger dimension. This paper examines the nature of spherically-symmetric random walks in detail. We perform a large-time asymptotic analysis of these random walks and use the results to determi...
متن کامل