Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Rao, Shravas"'
Autor:
Alev, Vedat Levi, Rao, Shravas
We study a variant of the down-up and up-down walks over an $n$-partite simplicial complex, which we call expanderized higher order random walks -- where the sequence of updated coordinates correspond to the sequence of vertices visited by a random w
Externí odkaz:
http://arxiv.org/abs/2405.08927
Autor:
Rao, Shravas
A matrix $\Phi \in \mathbb{R}^{Q \times N}$ satisfies the restricted isometry property if $\|\Phi x\|_2^2$ is approximately equal to $\|x\|_2^2$ for all $k$-sparse vectors $x$. We give a construction of RIP matrices with the optimal $Q = O(k \log(N/k
Externí odkaz:
http://arxiv.org/abs/2311.07889
Autor:
Rao, Shravas
This paper considers the Fourier transform over the slice of the Boolean hypercube. We prove a relationship between the Fourier coefficients of a function over the slice, and the Fourier coefficients of its restrictions. As an application, we prove a
Externí odkaz:
http://arxiv.org/abs/2111.03213
Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function $f$, $\bullet \quad \mathrm{deg}(f) = O(\widetilde{\mathrm{deg}}(f)^2)$: The degree of $f$ is at most quadratic in the approximate degree of $f$. This is op
Externí odkaz:
http://arxiv.org/abs/2010.12629
Let $\{W_t\}_{t=1}^{\infty}$ be a finite state stationary Markov chain, and suppose that $f$ is a real-valued function on the state space. If $f$ is bounded, then Gillman's expander Chernoff bound (1993) provides concentration estimates for the rando
Externí odkaz:
http://arxiv.org/abs/1906.07260
Autor:
Rao, Shravas
The celebrated Littlewood-Offord problem asks for an upper bound on the probability that the random variable $\epsilon_1 v_1 + \cdots + \epsilon_n v_n$ lies in the Euclidean unit ball, where $\epsilon_1, \ldots, \epsilon_n \in \{-1, 1\}$ are independ
Externí odkaz:
http://arxiv.org/abs/1904.13019
Autor:
Rao, Shravas
Let $A$ be an $N \times N$ Fourier matrix over $\mathbb{F}_p^{\log{N}/\log{p}}$ for some prime $p$. We improve upon known lower bounds for the number of rows of $A$ that must be sampled so that the resulting matrix $M$ satisfies the restricted isomet
Externí odkaz:
http://arxiv.org/abs/1903.12146
We give a short argument that yields a new lower bound on the number of subsampled rows from a bounded, orthonormal matrix necessary to form a matrix with the restricted isometry property. We show that a matrix formed by uniformly subsampling rows of
Externí odkaz:
http://arxiv.org/abs/1903.12135
Autor:
Rao, Shravas
Publikováno v:
Electronic Communications in Probability, Volume 24 (2019), paper no. 14
We prove deviation bounds for the random variable $\sum_{i=1}^{n} f_i(Y_i)$ in which $\{Y_i\}_{i=1}^{\infty}$ is a Markov chain with stationary distribution and state space $[N]$, and $f_i: [N] \rightarrow [-a_i, a_i]$. Our bound improves upon previo
Externí odkaz:
http://arxiv.org/abs/1806.11519
Autor:
Rao, Shravas, Regev, Oded
Consider an expander graph in which a $\mu$ fraction of the vertices are marked. A random walk starts at a uniform vertex and at each step continues to a random neighbor. Gillman showed in 1993 that the number of marked vertices seen in a random walk
Externí odkaz:
http://arxiv.org/abs/1703.10205