Random bistochastic matrices

Random bistochastic matrices

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

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...

Random Matrices and Random Boxes

OF THE DISSERTATION Random matrices and random boxes by Linh V. Tran Dissertation Director: Prof. Van Vu This thesis concerns two questions on random structures: the semi-circular law for adjacency matrix of regular random graph and the piercing number for random boxes. • Random matrices We proved in full generality the semi-circular law for random d-regular graph model in the case d tends to i...

Random Growth and Random Matrices

We give a survey of some of the recent results on certain two-dimensional random growth models and their relation to random matrix theory, in particular to the Tracy-Widom distribution for the largest eigenvalue. The problems are related to that of finding the length of the longest increasing subsequence in a random permutation. We also give a new approach to certain results for the Schur measu...

An Introduction to Random Matrices An Introduction to Random Matrices