Random antagonistic matrices

Random Antagonistic Matrices

The ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries Ai,j and Aj,i are real and have opposite signs, or are both zero, and the diagonal is zero. This generalization of antisymmetric matrices is suggested by the linearized dynamics of competitive species in ecology.

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

More about measures and Jacobians of singular random matrices

In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.