## 7 janvier 2021

Charles Frances (IRMA (Strasbourg))
Plongements grossiers et actions isométriques de groupes discrets

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Lieu : https://webconf.imo.universite-paris-saclay.fr/b/jer-7cp-7mk

Résumé : Le but de l’exposé est d’illustrer comment la notion de plongement grossier entre espaces métriques,
introduite par M. Gromov dans les années 80, permet de mieux comprendre les actions de groupes discrets préservant des structures géométriques rigides. On mettra l’accent sur l’étude du groupe des isométries
des variétés lorentziennes. On montrera une alternative de Tits pour ces groupes.

Notes de dernières minutes : Il n’y a pas de café culturel ce jeudi

Guillaume Lecué  (Crest - Ensae)
ROBUST SUBGAUSSIAN ESTIMATION OF A MEAN VECTOR IN NEARLY LINEAR TIME

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Résumé : Joint work with Jules Depersin.
Robust mean estimation has witnessed an increasing interest the last ten years in both statistics and computer sciences. We will first review the literature in this domain. Then, we will present the construction of an algorithm, running in time O(Nd+ uKd) , which is robust to outliers and heavy-tailed data and which achieves the subgaussian rate :
$$\sqrt(Tr(Σ)/N) + \sqrt( || Σ ||_op K/N )$$
with probability at least 1 -exp(c_0K)- ́exp(c_1u) where Σ is the covariance matrix of the informative data, K \in 1, . . . , N is some parameter (number of block means) and $u \in \N^*$ is another parameter of the algorithm. This rate is achieved when K \geq c_2 |O| where |O| is the number of outliers in the database and under the only assumption that the informative data have a second moment. The algorithm is fully data-dependent and does not use in its construction the proportion of outliers nor the rate above. Its construc- tion combines recently developed tools for Median-of-Means estimators and covering-Semi-definite Programming [1, 2]. We also show how this algorithm can automatically adapt to the number of outliers.
REFERENCES
[1] DIAKONIKOLAS, I., KAMATH, G., KANE, D., LI, J., MOITRA, A. and STEWART, A. (2019). Robust Es- timators in High-Dimensions Without the Computational Intractability. SIAM J. Comput. 48 742–864. MR3945261
[2] PENG, R., TANGWONGSAN, K. and ZHANG, P. (2012). Faster and Simpler Width-Independent Parallel Algorithms for Positive Semidefinite Programming.

Russell Lyons (Indiana University)
Random Walks on Dyadic Lattice Graphs and Their Duals

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Lieu : En ligne

Résumé : Dyadic lattice graphs and their duals are commonly used as discrete approximations to the hyperbolic plane. We use them to give examples of random rooted graphs that are stationary for simple random walk, but whose duals have only a singular stationary measure. This answers a question of Nicolas Curien and shows behaviour different from the unimodular case. The consequence is that planar duality does not combine well with stationary random graphs. We also study harmonic measure on dyadic lattice graphs and show its singularity. Much interesting behaviour observed numerically remains to be explained. No background will be assumed for the talk. This is joint work with Graham White.

janvier 2021 :
 Département de Mathématiques Bâtiment 307 Faculté des Sciences d'Orsay Université Paris-Saclay F-91405 Orsay Cedex Tél. : +33 (0) 1-69-15-79-56 Département Fermeture du département Laboratoire Formation