High-Dimensional Probability

Michaelmas Term 2021

Course description [PDF]

Course calendar

Problems [PDF]


[AdRBV] J. Arias-de-Reyna, K. Ball and R. Villa, Concentration of the distance in finite-dimensional normed spaces, Mathematika, 1998.

[BaL]  D. Bakry and M. Ledoux, Lévy-Gromov's isoperimetric inequality for an infinite-dimensional diffusion generator, Inventiones Mathematicae, 1996.

[BoL] S. Bobkov and M. Ledoux, Poincaré's inequalities and Talagrand's concentration phenomenon for the exponential distribution, Probability Theory and Related Fields, 1997.

[BLM] S. Boucheron, G. Lugosi and P. Massart, Concentration inequalities: a non-asymptotic theory of independence, Oxford University Press, 2013.

[GRS] N. Gozlan, C. Roberto and P. M. Samson, From dimension free concentration to Poincaré inequality, Calculus of Variations and PDE, 2015.

[LO] R. Latała and K. Oleszkiewicz, On the best constant in the Khinchin-Kahane inequality, Studia Mathematica, 1994.

[Led1] M. Ledoux, A short proof of the Gaussian isoperimetric inequality, Birkhäuser, 1998.

[Led2] M. Ledoux, The concentration of measure phenomenon, American Mathematical Society, 2001.

[PV] G. Paouris and P. Valettas, A Gaussian small deviation inequality for convex functions, Annals of Probability, 2018.

[Pis] G. Pisier, Probabilistic methods in the geometry of Banach spaces, Springer, 1986.

[Tal] M. Talagrand, Transportation cost for Gaussian and other product measures, Geometric and Functional Analysis, 1996.

[vH] R. van Handel, Probability in high dimensions, Available at https://web.math.princeton.edu/~rvan/APC550.pdf

[Ver] R. Vershynin, High-dimensional probability, Cambridge University Press, 2018, also available at https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.pdf.