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This paper deals with the union set of a stationary Poisson process of cylinders in $\mathbb{R}^n$ having an $(n-m)$-dimensional base and an $m$-dimensional direction space, where $m\in\{0,1,\ldots,n-1\}$ and $n\geq 2$. The concept…

Probability · Mathematics 2021-11-09 Carina Betken , Matthias Schulte , Christoph Thäle

We obtain an asymptotic formula with a power-saving error term for counting the integer points $(a,b,c,d)$ in an expanding box $[-X,X]^4$ that satisfy the determinant equation $x_1x_2-x_3x_4=r$ for $r \neq 0$ with two of entries to be…

Number Theory · Mathematics 2024-12-23 Rachita Guria

This paper presents a saddlepoint approximation of the random-coding union bound of Polyanskiy et al. for i.i.d. random coding over discrete memoryless channels. The approximation is single-letter, and can thus be computed efficiently.…

Information Theory · Computer Science 2014-04-28 Jonathan Scarlett , Alfonso Martinez , Albert Guillén i Fàbregas

Inspired by the boolean discrepancy problem, we study the following optimization problem which we term \textsc{Spherical Discrepancy}: given $m$ unit vectors $v_1, \dots, v_m$, find another unit vector $x$ that minimizes $\max_i \langle x,…

Computational Complexity · Computer Science 2019-11-19 Chris Jones , Matt McPartlon

Computational asymmetry, i.e., the discrepancy between the complexity of transformations and the complexity of their inverses, is at the core of one-way transformations. We introduce a computational asymmetry function that measures the…

Group Theory · Mathematics 2007-05-23 Jean-Camille Birget

The set of all error--correcting block codes over a fixed alphabet with $q$ letters determines a recursively enumerable set of rational points in the unit square with coordinates $(R,\delta)$:= (relative transmission rate, relative minimal…

Information Theory · Computer Science 2015-03-20 Yuri I. Manin , Matilde Marcolli

This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…

Numerical Analysis · Mathematics 2022-01-05 Molei Tao , Shi Jin

Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme…

Probability · Mathematics 2026-03-24 Ioan Scheffel , Marco Oesting , Gilles Stupfler

We develop new polynomial methods for studying systems of word equations. We use them to improve some earlier results and to analyze how sizes of systems of word equations satisfying certain independence properties depend on the lengths of…

Formal Languages and Automata Theory · Computer Science 2011-08-19 Aleksi Saarela

In this paper, long time and high order moment asymptotics for super-Brownian motions (sBm's) are studied. By using a moment formula for sBm's (e.g. Theorem 3.1, Hu et al. Ann. Appl. Probab. 2023+), precise upper and lower bounds for all…

Probability · Mathematics 2023-03-24 Yaozhong Hu , Xiong Wang , Panqiu Xia , Jiayu Zheng

We propose an extension of the Ewens measure on permutations by choosing the cycle weights to be asymptotically proportional to the degree of the symmetric group. This model is primarily motivated by a natural approximation to the so-called…

Probability · Mathematics 2019-07-30 Leonid V. Bogachev , Dirk Zeindler

This contribution presents an asymptotic formulation for the stick-slip behaviour of incomplete contacts under oscillatory variation of normal load, moment, shear load and differential bulk tension. The asymptotic description allows us not…

Soft Condensed Matter · Physics 2021-03-30 Hendrik Andresen , Rodolfo M. N. Fleury , Matthew R. Moore , David A. Hills

We recall the definition of the $\epsilon$-distortion complexity of a set defined in \cite{bcc} and the results obtained in this paper for Cantor sets of the interval defined by iterated function systems. We state an analogous definition…

Metric Geometry · Mathematics 2012-08-09 Pierre Collet

Among the fundamental questions in computer science is that of the impact of synchronism/asynchronism on computations, which has been addressed in various fields of the discipline: in programming, in networking, in concurrence theory, in…

Cellular Automata and Lattice Gases · Physics 2024-03-13 Isabel Donoso Leiva , Eric Goles , Martín Ríos-Wilson , Sylvain Sené

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, devising an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are…

Mathematical Physics · Physics 2011-10-18 Mikko Stenlund

In this paper, we develop a novel argument, the non-autonomous approximation method, to seek the asymptotic limits of the fully coupled multi-scale McKean-Vlasov stochastic systems with irregular coefficients, which, as summarized in…

Probability · Mathematics 2024-12-19 Yuewen Hou , Yun Li , Longjie Xie

This article is concerned with the asymptotic behavior of a 2D overhead crane. Taking into account the presence of a delay in the boundary, and assuming that no displacement term appears in the system, a distributed (interior) damping…

Analysis of PDEs · Mathematics 2018-04-19 Kaïs Ammari , Boumediène Chentouf

We study the convergence of a class of asymptotic preserving numerical schemes initially proposed by F. Filbet & S. Jin \cite{filb1} and G. Dimarco & L. Pareschi \cite{DimarcoP} in the context of nonlinear and stiff kinetic equations. Here,…

Numerical Analysis · Mathematics 2011-05-16 Francis Filbet , Amélie Rambaud

We consider the problem of tracking a target whose dynamics is modeled by a continuous It\=o semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds…

Probability · Mathematics 2015-10-16 Jiatu Cai , Mathieu Rosenbaum , Peter Tankov

During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be…

Optimization and Control · Mathematics 2023-02-10 Matúš Benko , Patrick Mehlitz