K. Tikhomirov

activity

20122026

most citedOn the spectral radius of a random matrix: an upper bound without fourth moment

25 citations · 89 across the 31 of their papers we have counts for

collaborators

Showing 2014Show all

3 papers · 1 filter

math.PR2014

The limit of the smallest singular value of random matrices with i.i.d. entries

Konstantin Tikhomirov

Let ${a_{ij}}$ $(1 \leq i, j < \infty)$ be i.i.d. real valued random variables with zero mean and unit variance and let an integer sequence $(N_{m})_{m = 1}^{\infty}$ satisfy $m/N_m\longrig…

math.PR2014

When does a discrete-time random walk in $R^{n}$ absorb the origin into its convex hull?

Konstantin Tikhomirov, Pierre Youssef

We connect this question to a problem of estimating the probability that the image of certain random matrices does not intersect with a subset of the unit sphere $S^{n - 1}$ …

math.PR2014★ 1 cited

The smallest singular value of random rectangular matrices with no moment assumptions on entries

Konstantin E. Tikhomirov

Let $δ > 1$ and $β > 0$ be some real numbers. We prove that there are positive $u, v, N_{0}$ depending only on $β$ and $δ$ with the following property: for any $N, n$ such that $N\ge \max(N…

The limit of the smallest singular value of random matrices with i.i.d. entries

When does a discrete-time random walk in Rn absorb the origin into its convex hull?

The smallest singular value of random rectangular matrices with no moment assumptions on entries

When does a discrete-time random walk in $R^{n}$ absorb the origin into its convex hull?