Author

K. Tikhomirov

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Preprint Sep 2026

The threshold for online balancing of i.i.d. binary vectors

Consider the task of online vector balancing for stochastic arrivals $X_1,\ldots,{X_T}$, where the $X_i$ are independent uniformly random $d$--sparse binary vectors in $\{0,1\}^n$. This is a random analogue of the online Beck--Fiala problem. We show that uniformly for $2\le d\le n/2$ and $T = \Theta(n)$, the optimal on...

Dylan J. Altschuler, K. Tikhomirov · 1 citation

Jul 2026

Level-set entropy and sparse randomized embeddings

This work develops an approach to the spectral norm of the matrix product $\Pi U_V$, based on entropy estimates for level sets of vectors $x\in V$, and shows that matching results hold for other random models with negatively associated entries.

K. Tikhomirov · arXiv.org · 0 citations