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DTSTART;VALUE=DATE:20171017T171500
DTEND;VALUE=DATE:20171017T171500
UID:5767@agenda.unifr.ch
DESCRIPTION: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,  \n$$\n\frac 1n \sum_{i=1}^n \boldsymbol{\vec x}_i \boldsymbol{\vec x}^*_i\n$$ \nhas an unbounded support as $N,n\to \infty$ and $\frac Nn\to c\in (0,\infty)$. As a consequence, its largest eigenvalue \n$$\n\lambda_{\max} \left( \frac 1n \sum_{i=1}^n \boldsymbol{\vec x}_i \boldsymbol{\vec x}^*_i\n\right)\n$$ \ngoes 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.<br/><br/>\nThis is a joint work with Peng Tian and Florence Merlevède.
SUMMARY:Prof. Jamal Najim (Université de Marne La Vallée): Large Random Matrices of Long Memory Stationary Processes: Asymptotics and fluctuations of the largest eigenvalue
CATEGORIES:Colloque / Congrès / Forum
LOCATION:PER 08\, Phys 2.52\, Chemin du Musée 3\, 1700 Fribourg
URL;VALUE=URI:https://agenda.unifr.ch/e/fr/5767
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