126 citations · 375 across the 42 of their papers we have counts for
5 papers · 1 filter
An extension of a Bourgain--Lindenstrauss--Milman inequality
Omer Friedland, Sasha Sodin
Let || . || be a norm on R^n. Averaging || (\eps_1 x_1, ..., \eps_n x_n) || over all the 2^n choices of \eps = (\eps_1, ..., \eps_n) in {-1, +1}^n, we obtain an expression ||| . ||…
Bounds on the concentration function in terms of Diophantine approximation
Omer Friedland, Sasha Sodin
We demonstrate a simple analytic argument that may be used to bound the Levy concentration function of a sum of independent random variables. The main application is a version of a…
Random matrices, non-backtracking walks, and orthogonal polynomials
Sasha Sodin
Several well-known results from the random matrix theory, such as Wigner's law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on…
An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies
Emanuel Milman, Sasha Sodin
We prove an isoperimetric inequality for the uniform measure on a uniformly convex body and for a class of uniformly log-concave measures (that we introduce). These inequalities im…
Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits
Shachar Lovett, Sasha Sodin
It is well known that R^N has subspaces of dimension proportional to N on which the \ell_1 norm is equivalent to the \ell_2 norm; however, no explicit constructions are known. Exte…