Rikhav Shah

activity

20182026

most citedDirected Random Geometric Graphs

9 citations · 14 across the 5 of their papers we have counts for

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Showing 2020Show all

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cs.DS2020

Smoothed analysis of the condition number under low-rank perturbations

Rikhav Shah, Sandeep Silwal

Let $M$ be an arbitrary $n$ by $n$ matrix of rank $n - k$ . We study the condition number of $M$ plus a \emph{low-rank} perturbation $U V^{T}$ where $U, V$ are $n$ by $k$ random Gaussian…

math.CO2020

Determinants of binary matrices achieve every integral value up to $Ω (2^{n} / n)$

Rikhav Shah

This work shows that the smallest natural number $d_{n}$ that is not the determinant of some $n \times n$ binary matrix is at least $c 2^{n} / n$ for $c = 1/201$ . That same quantity natura…

Smoothed analysis of the condition number under low-rank perturbations

Determinants of binary matrices achieve every integral value up to Ω(2n/n)

Determinants of binary matrices achieve every integral value up to $Ω (2^{n} / n)$