Related papers: Strong Borel--Cantelli Lemmas for Recurrence
We develop sufficient analytic conditions for recurrence and transience of non-sectorial perturbations of possibly non-symmetric Dirichlet forms on a general state space. These form an important subclass of generalized Dirichlet forms which…
We present an information theoretic proof of the nonsignalling multiprover parallel repetition theorem, a recent extension of its two-prover variant that underlies many hardness of approximation results. The original proofs used de Finetti…
We establish quantitative results for the statistical be\-ha\-vi\-our of \emph{infinite systems}. We consider two kinds of infinite system: i) a conservative dynamical system $(f,X,\mu)$ preserving a $\sigma$-finite measure $\mu$ such that…
A conjecture of Erd\H{o}s states that for any infinite set $A \subseteq \mathbb R$, there exists $E \subseteq \mathbb R$ of positive Lebesgue measure that does not contain any nontrivial affine copy of $A$. The conjecture remains open for…
We prove an asymptotic formula for the recurrence coefficients of orthogonal polynomials with orthogonality measure $\log \bigl(\frac{2}{1-x}\bigr) {\rm d}x$ on $(-1,1)$. The asymptotic formula confirms a special case of a conjecture by…
We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khintchine's recurrence theorem obtained by Bergelson in the measure theoretic case. A noncommutative…
Using a result of Behrend concerning sets without arithmetic progressions, we construct some examples of dynamical systems with slow time of multiple recurrence. Our theorem is a quatitative analog of Furstenberg's Correspondence Principle.
In this paper, we consider recurrence sequences $x_n=\xi_1 \alpha_1^n+\xi_2 \alpha_2^n$ ($n=0,1,\ldots$) with companion polynomial $P(X)$. For example, the sequence $x_n=\xi_1(4+\sqrt{2})^n+\xi_2(4-\sqrt{2})^n$ satisfies the recurrence…
Let $(M,g)$ be a compact, connected Riemannian manifold of dimension $n\ge 2$, and let $\{e_j\}_{j=0}^\infty$ be an orthonormal basis of Laplace eigenfunctions $-\Delta_g e_j=\lambda_j^2 e_j$. Given a finite Borel measure $\mu$ on $M$,…
We consider a classical system of point particles interacting by means of a short range potential. We prove that, in the low--density (Boltzmann--Grad) limit, the system behaves, for short times, as predicted by the associated Boltzmann…
Recovering probability measures from moments is a central theme in statistics and optimization. In particular, we focus on the recovery of measures from moments and pseudo-moments, which may come from solving the moment-SOS hierarchy in one…
We handle divergent {\epsilon} expansions in different universality classes derived from modified Landau-Wilson Hamiltonian. Landau-Wilson Hamiltonian can cater for describing critical phenomena on a wide range of physical systems which…
In "IP-sets and polynomial recurrence", Bergelson, Furstenberg, and McCutcheon established the following far reaching extension of Khintchine's recurrence theorem: For any invertible probability preserving system $(X,\mathcal A,\mu,T)$, any…
On a polarized manifold $(X,L)$, the Bergman iteration $\phi_k^{(m)}$ is defined as a sequence of Bergman metrics on $L$ with two integer parameters $k, m$. We study the relation between the K\"ahler-Ricci flow $\phi_t$ at any time $t \geq…
The study of sequences of polynomials satisfying high order recurrence relations is connected with the asymptotic behavior of multiple orthogonal polynomials, the convergence properties of type II Hermite-Pad\'e approximation, and…
By using various expansions of the parametric digamma function and the method of residue computations, we study three variants of the linear Euler sums, related Hoffman's double $t$-values and Kaneko-Tsumura's double $T$-values, and…
Recursive Monte Carlo filters, also called particle filters, are a powerful tool to perform computations in general state space models. We discuss and compare the accept--reject version with the more common sampling importance resampling…
We consider the problem of reconstructing energies, momenta, and masses in collider events with missing energy, along with the complications introduced by combinatorial ambiguities and measurement errors. Typically, one reconstructs more…
Consider $\{p_n\}_{n=0}^{\infty}$, a sequence of polynomials orthogonal with respect to $w(x)>0$ on $(a,b)$, and polynomials $\{g_{n,k}\}_{n=0}^{\infty},k \in \mathbb{N}_0$, orthogonal with respect to $c_k(x)w(x)>0$ on $(a,b)$, where…
Our main aim in this self-contained article is at the same time to detail the relationships between the resurgence and the hyperasymptotic theories, and to demonstrate how these theories can be used for an implicit resurgent function. For…