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REPORTS > KEYWORD > EXPANDER WALKS:
Reports tagged with expander walks:
TR10-072 | 19th April 2010
Russell Impagliazzo, Valentine Kabanets

Constructive Proofs of Concentration Bounds

We give a simple combinatorial proof of the Chernoff-Hoeffding concentration bound~\cite{Chernoff, Hof63}, which says that the sum of independent $\{0,1\}$-valued random variables is highly concentrated around the expected value. Unlike the standard proofs,
our proof does not use the method of higher moments, but rather uses a simple ... more >>>


TR21-091 | 29th June 2021
Gil Cohen, Dor Minzer, Shir Peleg, Aaron Potechin, Amnon Ta-Shma

Expander Random Walks: The General Case and Limitations

Cohen, Peri and Ta-Shma (STOC'21) considered the following question: Assume the vertices of an expander graph are labelled by $\pm 1$. What "test" functions $f : \{\pm 1\}^t \to \{\pm1 \}$ can or cannot distinguish $t$ independent samples from those obtained by a random walk? [CPTS'21] considered only balanced labelling, ... more >>>


TR22-024 | 17th February 2022
Louis Golowich, Salil Vadhan

Pseudorandomness of Expander Random Walks for Symmetric Functions and Permutation Branching Programs

Revisions: 1

We study the pseudorandomness of random walks on expander graphs against tests computed by symmetric functions and permutation branching programs. These questions are motivated by applications of expander walks in the coding theory and derandomization literatures. We show that expander walks fool symmetric functions up to a $O(\lambda)$ error in ... more >>>


TR22-027 | 22nd February 2022
Guy Blanc, Dean Doron

New Near-Linear Time Decodable Codes Closer to the GV Bound

Revisions: 1

We construct a family of binary codes of relative distance $\frac{1}{2}-\varepsilon$ and rate $\varepsilon^{2} \cdot 2^{-\log^{\alpha}(1/\varepsilon)}$ for $\alpha \approx \frac{1}{2}$ that are decodable, probabilistically, in near linear time. This improves upon the rate of the state-of-the-art near-linear time decoding near the GV bound due to Jeronimo, Srivastava, and Tulsiani, who ... more >>>


TR22-181 | 15th December 2022
Louis Golowich

A New Berry-Esseen Theorem for Expander Walks

Revisions: 1

We prove that the sum of $t$ boolean-valued random variables sampled by a random walk on a regular expander converges in total variation distance to a discrete normal distribution at a rate of $O(\lambda/t^{1/2-o(1)})$, where $\lambda$ is the second largest eigenvalue of the random walk matrix in absolute value. To ... more >>>


TR24-118 | 9th July 2024
Amnon Ta-Shma, Ron Zadiario

The Expander Hitting Property When the Sets Are Arbitrarily Unbalanced

Numerous works have studied the probability that a length $t-1$ random walk on an expander is confined to a given rectangle $S_1 \times \ldots \times S_t$, providing both upper and lower bounds for this probability.
However, when the densities of the sets $S_i$ may depend on the walk length (e.g., ... more >>>




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