17
Oct

## Prof. Jamal Najim (Université de Marne La Vallée): Large Random Matrices of Long Memory Stationary Processes: Asymptotics and fluctuations of the largest eigenvalue

Academic or specialist Colloquium / Congress / Forum
17.10.2017 17:15
Onsite

Given $n$ i.i.d. samples $(\boldsymbol{\vec x}_1, \cdots, \boldsymbol{\vec x}_n)$ of a $N$-dimensional long memory stationary process, it has recently been proved that the limiting spectral distribution of the sample covariance matrix,
$$\frac 1n \sum_{i=1}^n \boldsymbol{\vec x}_i \boldsymbol{\vec x}^*_i$$
has an unbounded support as $N,n\to \infty$ and $\frac Nn\to c\in (0,\infty)$. As a consequence, its largest eigenvalue
$$\lambda_{\max} \left( \frac 1n \sum_{i=1}^n \boldsymbol{\vec x}_i \boldsymbol{\vec x}^*_i \right)$$
goes to infinity. In this talk, we will describe its asymptotics and fluctuations, tightly related to the features of the underlying population covariance matrix, which is of a Toeplitz nature.

This is a joint work with Peng Tian and Florence Merlevède.

When? 17.10.2017 17:15 PER 08 Phys 2.52Chemin du Musée 31700 Fribourg Department of Mathematicsisabella.schmutz@unifr.ch
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