Related papers: An explicit two-source extractor with min-entropy …
We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy…
In successive refinement of information, the decoder refines its representation of the source progressively as it receives more encoded bits. The rate-distortion region of successive refinement describes the minimum rates required to attain…
(Abridged) We present a new method for detecting and measuring compact sources in conditions of intense, and highly variable, fore/background. While all most commonly used packages carry out the source detection over the signal image, our…
Blasiok (SODA'18) recently introduced the notion of a subgaussian sampler, defined as an averaging sampler for approximating the mean of functions $f:\{0,1\}^m \to \mathbb{R}$ such that $f(U_m)$ has subgaussian tails, and asked for explicit…
It is well established that the notion of min-entropy fails to satisfy the \emph{chain rule} of the form $H(X,Y) = H(X|Y)+H(Y)$, known for Shannon Entropy. Such a property would help to analyze how min-entropy is split among smaller blocks.…
The purpose of this expository note is to give the proof of a theorem of Bourgain with some additional details and updated notation. The theorem first appeared as an appendix to the breakthrough paper by Friedgut, \emph{Sharp Thresholds of…
We characterize a new mid-infrared frequency comb generator based on difference frequency generation around 3.2 microns. High power per comb mode (>10-7 W/mode) is obtained over a broad spectral span (>700 nm). The source is used for direct…
Given a Boolean function $f:\{-1,1\}^n\to \{-1,1\}$, the Fourier distribution assigns probability $\widehat{f}(S)^2$ to $S\subseteq [n]$. The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai asks if there exist a universal…
The notion of semi-random sources, also known as Santha-Vazirani (SV) sources, stands for a sequence of n bits, where the dependence of the i'th bit on the previous i-1 bits is limited for every $i\in[n]$. If the dependence of the i'th bit…
A recent experiment showed that, contrary to theoretical predictions, beyond a cutoff point grinding coffee more finely results in lower extraction. One potential explanation for this is that fine grinding promotes non-uniform extraction in…
Kyurkchiev and Andreev (1985) constructed an infinite sequence of Weierstrass-type iterative methods for approximating all zeros of a polynomial simultaneously. The first member of this sequence of iterative methods is the famous method of…
Post-processing of the raw bits produced by a true random number generator (TRNG) is always necessary when the entropy per bit is insufficient for security applications. In this paper, we derive a tight bound on the output min-entropy of…
We find a sharp combinatorial bound for the metric entropy of sets in R^n and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central…
The entropy accumulation theorem states that the smooth min-entropy of an $n$-partite system $A = (A_1, \ldots, A_n)$ is lower-bounded by the sum of the von Neumann entropies of suitably chosen conditional states up to corrections that are…
The expressions for entropy production, free energy, and entropy extraction rates are derived for a Brownian particle that walks in an underdamped medium. Our analysis indicates that as long as the system is driven out of equilibrium, it…
It is shown that Schr\"odinger maximal inequalities over fractals are equivalent to the $L^2$ decay rates of Fourier transforms of fractal measures over the paraboloid. A similar connection is shown between the wave equation and cone…
We investigate 2-variable expanders and 3-source extractors in prime fields. We extend previous results of J. Bourgain.
We establish an exponential error term for the renewal theorem in the context of products of random matrices, which is surprising compared with classical abelian cases. A key tool is the Fourier decay of the Furstenberg measures on the…
Obtaining a non-trivial (super-linear) lower bound for computation of the Fourier transform in the linear circuit model has been a long standing open problem. All lower bounds so far have made strong restrictions on the computational model.…
Obtaining a non-trivial (super-linear) lower bound for computation of the Fourier transform in the linear circuit model has been a long standing open problem for over 40 years. An early result by Morgenstern from 1973, provides an $\Omega(n…