Related papers: A general lower bound for the asymptotic convergen…
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire,…
We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton Jacobi Bellman Equations by introducing a new notion of consistency. We apply our general…
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…
We give asymptotic estimates for the number of non-overlapping homothetic copies of some centrally symmetric oval $B$ which have a common point with a 2-dimensional domain $F$ having rectifiable boundary, extending previous work of the…
We derive lower bounds for the $L^p(\mu)$ norms of monic extremal polynomials with respect to compactly supported probability measures $\mu$. We obtain a sharp universal lower bound for all $0<p<\infty$ and all measures in the Szeg\H{o}…
Asymptotic formula is derived for the behavior of the fundamental solution of the second-order elliptic self-adjoint operator with a piecewise-smooth coefficient in front of the senior derivatives near the discontinuity surface of the…
The Cantor ladder is naturally included into various families of self-similar functions. In the frame of these families we study the asymptotics of some parametric integrals.
We compute the minimal exponent of the affine cone over a complete intersection of smooth projective hypersurfaces intersecting transversely. The upper bound for the minimal exponent is proved, more generally, in the weighted homogeneous…
We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our…
We obtain an explicit simple formula for the coefficients of the asymptotic expansion for the factorial of a natural number,in terms of derivatives of powers of an elementary function. The unique explicit expression for the coefficients…
We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.
We present general prescriptions for the asymptotic expansion of massive multi-loop Feynman integrals near threshold. As in the case of previously known prescriptions for various limits of momenta and masses, the terms of the threshold…
We derive asymptotic formulas for central extended binomial coefficients, which are generalizations of binomial coefficients. To do so, we relate the exact distribution of the sum of independent discrete uniform random variables to the…
Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that R-rank(S) is at least 2, and let $\Gamma$ be a uniform lattice in G. (a) If $CH$ holds, then $\Gamma$ has a unique asymptotic cone up to…
In this paper we provide new compact integral expressions and associated simple asymptotic approximations for converse and achievability bounds in the finite blocklength regime. The chosen converse and random coding union bounds were taken…
The paper considers estimates for the asymptotics of summation functions of bounded multiplicative arithmetic functions. Several assertions on this subject are proved and examples are considered.
This paper classifies the factorizations of almost simple groups with a factor having at least two nonsolvable composition factors. This together with a previous classification result of the authors reduces the factorization problem of…
We give asymptotics for the cumulative distribution function (CDF) for degrees of large dense random graphs sampled from a graphon. The proof is based on precise asymptotics for binomial random variables. Replacing the indicator function in…
We provide several asymptotic expansions of the prime counting function $\pi(x)$ and related functions. We define an {\it asymptotic continued fraction expansion} of a complex-valued function of a real or complex variable to be a possibly…