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PR ] 3 0 O ct 2 01 9 MATRIX POINCARÉ INEQUALITIES AND CONCENTRATION
| Content Provider | Semantic Scholar |
|---|---|
| Author | Aoun, Richard Banna, Marwa Youssef, Pierre |
| Copyright Year | 2019 |
| Abstract | We show that any probability measure satisfying a Matrix Poincaré inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carré du champ operator. This extends to the noncommutative setting a classical phenomenon in the scalar case. Moreover, the proof gives rise to new matrix trace inequalities which could be of independent interest. We then apply this general fact by establishing matrix Poincaré inequalities to derive matrix concentration inequalities for Gaussian measures, product measures and for Strong Rayleigh measures. The latter represents the first instance of matrix concentration for general matrix functions of negatively dependent random variables. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://export.arxiv.org/pdf/1910.13797 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
