Seminar by Benjamin Landon

Probability seminar series 

Benjamin Landon
University of Toronto

Room: M3 3127

Maximum of the characteristic polynomial of i.i.d. random matrices

The characteristic polynomial of a large random matrix with i.i.d. entries is an example of a logarithmically correlated field. In the special case of the complex Ginibre ensemble, in which the matrix consists of Gaussian entries, Lambert computed the leading order asymptotics of the maximum of this field.

In this talk we discuss the extension of this result to general random matrices, not necessarily having Gaussian entries, via a branching random walk representation for the logarithm of the characteristic polynomial.