Related papers: Furstenberg-type estimates under mild non-concentr…

We study the $\delta$-discretized Szemer\'edi-Trotter theorem and Furstenberg set problem. We prove sharp estimates for both two problems assuming tubes satisfy some spacing condition. For both two problems, we construct sharp examples that…

We prove essentially sharp incidence estimates for a collection of $\delta$-tubes and $\delta$-balls in the plane, where the $\delta$-tubes satisfy an $\alpha$-dimensional spacing condition and the $\delta$-balls satisfy a…

We use recent advances in the theory of Furstenberg sets to prove new incidence results of Szemer\'edi--Trotter strength for $\delta$-discretized structures with Cartesian product flavor. We use these results to make progress on a number of…

A \emph{double extrema form} of the calculus of variations is put forward in which only the smallest one of the finite differences is physically meaningful to represent the variational derivatives defined on the discrete points. The most…

We obtain moderate deviations theorems and exponential (Bernstein type) concentration inequalities for "nonconventional" sums of the form $S_N=\sum_{n=1}^N (F(\xi_{q_1(n)},\xi_{q_2(n)},...,\xi_{q_\ell(n)})-\bar F)$.

We prove two-ends Furstenberg estimates in the plane for a Katz-Tao $(\delta,t)$-set of lines, for general $t\in[0,2]$.

We consider the large deviations associated with the empirical mean of independent and identically distributed random variables under a subexponential moment condition. We show that non-trivial deviations are observable at a subexponential…

We prove a Bennett-type concentration bound for suprema of empirical processes based on sampling without replacement and a corresponding bound in the case of an arbitrary Hoeffding statistics. We improve on the previous results of such…

We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…

We study large deviations for the time average of the Ornstein-Uhlenbeck process raised to an arbitrary power. We prove that beyond a critical value, large deviations are subexponential in time, with a non-convex rate function whose main…

We give a lower bound for the size of a subset of $\mathbb F_q^n$ containing a rich k-plane in every direction, a k-plane Furstenberg set. The chief novelty of our method is that we use arguments on non-reduced subschemes and flat families…

According to Bell's theorem a large class of hidden-variable models obeying Bell's notion of local causality conflict with the predictions of quantum mechanics. Recently, a Bell-type theorem has been proven using a weaker notion of local…

This paper focuses on the strong convergence of the truncated $\theta$-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate,…

We investigate the asymptotic behavior of Bayesian posterior distributions under independent and identically distributed ($i.i.d.$) misspecified models. More specifically, we study the concentration of the posterior distribution on…

We provide a very simple case showing that the weak form of the Heisenberg limit can be beaten while the prior information is improved without bias.

We present some new nonparametric estimators of entropies and we establish almost sure consistency and central limit Theorems for some of the most important entropies in the discrete case. Our theorical results are validated by simulations.

This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a…

A non-quantitative version of the Freiman-Ruzsa theorem is obtained for finite stable sets with small tripling in arbitrary groups, as well as for (finite) weakly normal subsets in abelian groups.

We give a revised version of Schmidt's treatment of forms in many variables, which allows us to prove a Hasse principle under more lenient conditions on the number of variables than what had previously been thought possible with these…

In this paper we prove some lower bounds on the Hausdorff dimension of sets of Furstenberg type. Moreover, we extend these results to sets of generalized Furstenberg type, associated to doubling dimension functions. With some additional…