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We consider the regular balanced model of formula generation in conjunctive normal form (CNF) introduced by Boufkhad, Dubois, Interian, and Selman. We say that a formula is $p$-satisfying if there is a truth assignment satisfying…
We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.
Model approximations are common practice when estimating structural or quasi-structural models. The paper considers the econometric properties of estimators that utilize projections to reimpose information about the exact model in the form…
By a profound result of Heinrich, Novak, Wasilkowski, and Wo{\'z}niakowski the inverse of the star-discrepancy $n^*(s,\ve)$ satisfies the upper bound $n^*(s,\ve) \leq c_{\mathrm{abs}} s \ve^{-2}$. This is equivalent to the fact that for any…
Using methods from classical analysis, sharp bounds for the ratio of differences of Power Means are obtained. Our results generalize and extend previous ones due to S. Wu(2005), and to S. Wu and L. Debnath.
This study introduces a correction to the approximation of effective degrees of freedom as proposed by Satterthwaite (1941, 1946), specifically addressing scenarios where component degrees of freedom are small. The correction is grounded in…
We address the problem of producing a lower bound for the mean of a discrete probability distribution, with known support over a finite set of real numbers, from an iid sample of that distribution. Up to a constant, this is equivalent to…
Measurements take a singular role in quantum theory. While they are often idealized as an instantaneous process, this is in conflict with all other physical processes in nature. In this Letter, we adopt a standpoint where the interaction…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
We fix a gap in the proof of a result in our earlier paper arXiv:1908.09548
Summary of a talk at the conference The Chaotic Universe in Rome, Feb, 1999
Correction for Error estimates for binomial approximations of game options [math.PR/0607123]
We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…
The best current estimates of the thresholds for the existence of solutions in random constraint satisfaction problems ('CSPs') mostly derive from the first and the second moment method. Yet apart from a very few exceptional cases these…
We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit…
We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…
There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
We show that the lower bound to the critical fraction of data needed to infer (learn) the orientation of the anisotropy axis of a probability distribution, determined by Herschkowitz and Opper [Phys.Rev.Lett. 86, 2174 (2001)], is not always…
This is a reply to arXiv:1409.7513 [Phys. Rev. Lett. 113, 138901 (2014)].