Abstract: Two concepts of symmetry for the distributions of positive random variables Y are log-symmetry (symmetry of the distribution of log Y ) and R-symmetry ([7]). In this paper, we characterise the distributions that have both properties, which we call doubly symmetric. It turns out that doubly symmetric distributions constitute a subset of those distributions that are moment-equivalent to...

Two concepts of symmetry for the distributions of positive random variables Y are log-symmetry (symmetry of the distribution of log Y ) and Rsymmetry (Mudholkar & Wang, 2007). In this paper, we characterise the distributions that have both properties, which we call doubly symmetric. It turns out that doubly symmetric distributions constitute a subset of those distributions that are moment-equiv...

Two concepts of symmetry for the distributions of positive random variables Y are log-symmetry (symmetry of the distribution of log Y ) and Rsymmetry (Mudholkar & Wang, 2007). In this paper, we characterise the distributions that have both properties, which we call doubly symmetric. It turns out that doubly symmetric distributions constitute a subset of those distributions that are moment-equiv...

We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled)Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)-entry of the fundamental matrices of the Markov chains induced by the same policies. In particular, we focus on the subset of these policies that induce doubly stochastic probability tran...

Let A ∈ Ωn be doubly-stochastic n × n matrix. Alexander Schrijver proved in 1998 the following remarkable inequality per(Ã) ≥ ∏ 1≤i,j≤n (1−A(i, j)); Ã(i, j) =: A(i, j)(1−A(i, j)), 1 ≤ i, j ≤ n (1) We prove in this paper the following generalization (or just clever reformulation) of (1): For all pairs of n × n matrices (P,Q), where P is nonnegative and Q is doublystochastic log(per(P )) ≥ ∑ 1≤i,...

We ask several questions on the structure of the polytope of doubly stochastic n n matrices Pn, known as a Birkhoo polytope. We discuss the volume of Pn, the work of the simplex method, and the mixing of random walks Pn.

Mathematics Subject Classification (2000): 53C25, 53C40, 53C42.

We claim that both of these walks have the same mixing time. This fact is in fact true for any Markov chain on groups. In this case note that we are considering a Markov chain on the symmetric group Sn. In general consider any group G and suppose we have a set of generators {g1, . . . , gk}. In each time step we choose a generator from this set according to a probability distribution μ and we a...

We introduce another view of sequence evolution. Contrary to other approaches, we model the substitution process in two steps. First we assume (arbitrary) scaled branch lengths on a given phylogenetic tree. Second we allocate a Poisson distributed number of substitutions on the branches. The probability to place a mutation on a branch is proportional to its relative branch length. More importan...