Related papers: Logarithm laws for BCZ map
Using the techniques developed in arxiv: 1203.3544 we compute the universal part of the equilibrium partition function characteristic of a theory with multiple abelian U(1) anomalies in arbitrary even spacetime dimensions. This contribution…
We study non-Birkhoff periodic orbits in symmetric convex planar billiards. Our main result provides a quantitative criterion for the existence of such orbits with prescribed minimal period, rotation number, and spatiotemporal symmetry. We…
We construct a simple symplectic map to study the dynamics of eccentric orbits in non-spherical potentials. The map offers a dramatic improvement in speed over traditional integration methods, while accurately representing the qualitative…
A classical Borel Cantelli Lemma gives conditions for deciding whether an infinite number of rare events will almost surely happen. In this article, we propose an extension of Borel Cantelli Lemma to characterize the multiple occurrence of…
We introduce an algebra model to study higher order sum rules for orthogonal polynomials on the unit circle. We build the relation between the algebra model and sum rules, and prove an equivalent expression on the algebra side for the sum…
We prove that an ordinary Dirichlet series with coefficients a(n)=g(n b) has an abscissa of convergence 0 if g is an odd 1-periodic, real-analytic function and b is Diophantine. We also show that if g is odd and has bounded variation and b…
In this paper, we obtain a Carleman estimate for the higher order partial differential operator. In the process of establishing this estimate, we developed a new method, which is called the back-propagation method (the BPM, for short). This…
We survey some of the recent developments in the study of logarithm laws and shrinking target properties for various families of dynamical systems. We discuss connections to geometry, diophantine approximation, and probability theory.
We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional L\'{e}vy's modulus of continuity and many other results are its particular cases.…
We present several applications of the pathwise Burkholder-Davis-Gundy (BDG) inequalities. Most importantly we prove them for cadlag semimartingales and a general function $\Phi$, and use this to derive BDG inequalities (non-pathwise ones)…
An existence of an aperiodic point for outer billiard outside regular dodecagon is proved. Additionally, almost all orbits of such an outer billiard are proved to be periodic, and all possible periods are listed explicitly. The proof is…
Roth type irrational rotation numbers have several equivalent arithmetical characterizations as well as several equivalent characterizations in terms of the dynamics of the corresponding circle rotations. In this paper we investigate how to…
Zero-one laws are a central topic in metric Diophantine approximation. A classical example of such laws is the Borel-Bernstein theorem. In this note, we prove a complex analogue of the Borel-Bernstein theorem for complex Hurwitz continued…
We present equations of motion for charged particles using balanced equations, and without introducing explicitly divergent quantities. This derivation contains as particular cases some well known equations of motion, as the Lorentz-Dirac…
We consider the Blandford-Znajek (BZ) mechanism for extracting black hole spin energy to drive astrophysical jets. Analyses of the BZ mechanism generally take no account of any electric charge on the black hole. But, as noted by Wald and…
The repartition of dense orbits of $\textrm{SL}(2,\dr Z)$ in the euclidean plane is described by Ledrappier and Nogueira. We describe here the specific patterns one can see by experimentation, linking it to diophantine approximation theory.
Explicit algebraic area enumeration formulae are derived for various lattice walks generalizing the canonical square lattice walk, and in particular for the triangular lattice chiral walk recently introduced by the authors. A key element in…
We derive strong laws of large numbers and central limit theorems for Bajraktarevi\'c, Gini and exponential- (also called Beta-type) and logarithmic Cauchy quotient means of independent identically distributed (i.i.d.) random variables. The…
The Bulgarian Solitaire rule induces a finite dynamical system on the set of integer partitions of $n$. Brandt characterized and counted all cycles in its recurrent set for any given $n$, with orbits parametrized by necklaces of black and…
Let $x \mapsto x+ \alpha$ be a rotation on the circle and let $\varphi$ be a step function. We denote by $\varphi\_n (x)$ the corresponding ergodic sums $\sum\_{j=0}^{n-1} \varphi(x+j \alpha)$. Under an assumption on $\alpha$, for example…