Related papers: Hyperbolic Concentration, Anti-concentration, and …
This paper mainly discuss the regularity behavior of the hyperbolic magnetic Schroedinger equation with singular coefficients near the origin. We apply the techniques from the microlocal analysis to explore the upper bound of loss of…
As charged particles surpass the speed of light in an optical medium they produce radiation - analogously to the way jet planes surpass the speed of sound and produce a sonic boom. This radiation emission, known as the Cherenkov effect, is…
We utilize operational methods to generalize the Chernoff inequality and prove a new result that relates the moment bound to strictly absolute monotonic functions. We show that the Chernoff bound is part of a continuum of probability…
We describe the general setting for the optical Aharonov-Bohm effect based on the inverse problem of the identification of the coefficients of the governing hyperbolic equation by the boundary measurements. We interpret the inverse problem…
We show that the Consensus Division theorem implies lower bounds on the chromatic number of Kneser hypergraphs, offering a novel proof for a result of Alon, Frankl, and Lov\'{a}sz (Trans. Amer. Math. Soc., 1986) and for its generalization…
This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…
In this article, we improve the classical Bukhgeim-Klibanov method presented in [1],which can be used to prove the conditional stability of inverse source problem for a hyperbolic equation from the measurement on the subboundary. A major…
Choosing models from a hypothesis space is a frequent task in approximation theory and inverse problems. Cross-validation is a classical tool in the learner's repertoire to compare the goodness of fit for different reconstruction models.…
Concentration inequalities are fundamental tools in probabilistic combinatorics and theoretical computer science for proving that random functions are near their means. Of particular importance is the case where f(X) is a function of…
Relating to finding possible upper bounds for the probability of error for discriminating between two quantum states, it is well-known that \begin{align*} \mathrm{tr}(A+B) - \mathrm{tr}|A-B|\leq 2\, \mathrm{tr}\big(f(A)g(B)\big)…
Discriminating between noisy quantum processes is a central primitive for quantum communication, metrology, and computing. While discrimination limits for finite-dimensional channels are well understood, the continuous-variable setting,…
In Bayesian probabilistic programming, a central problem is to estimate the normalised posterior distribution (NPD) of a probabilistic program with conditioning via score (a.k.a. observe) statements. Most previous approaches address this…
The main goal of this paper is to study the discretization problem for the hyperbolic cross trigonometric polynomials. This important problem turns out to be very difficult. In this paper we begin a systematic study of this problem and…
In this paper, the hyperbolic Anderson equation generated by a time-dependent Gaussian noise is under investigation in two fronts: The solvability and large-$t$ asymptotics. The investigation leads to a necessary and sufficient condition…
We study the relative entropy of the empirical probability vector with respect to the true probability vector in multinomial sampling of $k$ categories, which, when multiplied by sample size $n$, is also the log-likelihood ratio statistic.…
Active learning can reduce the number of samples needed to perform a hypothesis test and to estimate the parameters of a model. In this paper, we revisit the work of Chernoff that described an asymptotically optimal algorithm for performing…
The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we provide expressions for its moments of arbitrary order…
This paper derives confidence intervals (CI) and time-uniform confidence sequences (CS) for the classical problem of estimating an unknown mean from bounded observations. We present a general approach for deriving concentration bounds, that…
We prove a conditional theorem on the positivity of the Lyapunov exponent for a Schr\"odinger cocycle over a skew shift base with a cosine potential and the golden ratio as frequency. For coupling below 1, which is the threshold for…
It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such…