Random bistochastic matrices
نویسندگان
چکیده
1 ‘Mark Kac’ Complex Systems Research Centre, Uniwersytet Jagielloński, ul. Reymonta 4, 30-059 Kraków, Poland 2 Fachbereich Physik, Universität Duisburg-Essen, Campus Duisburg, 47048 Duisburg, Germany 3 Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, ul. Reymonta 4, 30-059 Kraków, Poland 4 Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotników 32/44, 02-668 Warszawa, Poland
منابع مشابه
Central Limit Theorem and recurrence for random walks in bistochastic random environments
We prove the annealed Central Limit Theorem for random walks in bistochastic random environments on Zd with zero local drift. The proof is based on a “dynamicist’s interpretation” of the system, and requires a much weaker condition than the customary uniform ellipticity. Moreover, recurrence is derived for d ≤ 2. Mathematics Subject Classification: 60G50, 60K37, 37A50 (60F05, 60G42, 37A20, 37H9...
متن کاملVolume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant
A bistochastic matrix B of size N is called unistochastic if there exists a unitary U such that Bij = Uij 2 for i , j=1, . . . ,N. The set U3 of all unistochastic matrices of order N=3 forms a proper subset of the Birkhoff polytope, which contains all bistochastic doubly stochastic matrices. We compute the volume of the set U3 with respect to the flat Lebesgue measure and analytically evaluate ...
متن کاملar X iv : 0 90 9 . 01 16 v 1 [ m at h - ph ] 1 S ep 2 00 9 Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant
A bistochastic matrix B of size N is called unistochastic if there exists a uni-tary U such that B ij = |U ij | 2 for i, j = 1,. .. , N. The set U 3 of all unistochastic matrices of order N = 3 forms a proper subset of the Birkhoff polytope, which contains all bistochastic (doubly stochastic) matrices. We compute the volume of the set U 3 with respect to the flat (Lebesgue) measure and analytic...
متن کاملComposition of quantum states and dynamical subadditivity
We introduce a composition of quantum states of a bipartite system which is based on the reshuffling of density matrices. This non-Abelian product is associative and stems from the composition of quantum maps acting on a simple quantum system. It induces a semi-group in the subset of states with maximally mixed partial traces. Subadditivity of the von Neumann entropy with respect to this produc...
متن کاملBirkhoff ’ S Polytope and Unistochastic Matrices N = 3 and N = 4
The set of bistochastic or doubly stochastic N × N matrices form a convex set called Birkhoff’s polytope, that we describe in some detail. Our problem is to characterize the set of unistochastic matrices as a subset of Birkhoff’s polytope. For N = 3 we present fairly complete results. For N = 4 partial results are obtained. An interesting difference between the two cases is that there is a ball...
متن کامل