Related papers: Metric discrepancy results for geometric progressi…
We prove the law of the iterated logarithm for discrepancies of the sequence $\{(3/2)^kx\}$.
We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes.…
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…
We derive general results on the small deviation behavior for some classes of iterated processes. This allows us, in particular, to calculate the rate of the small deviations for $n$-iterated Brownian motions and, more generally, for the…
Let S_1(n),...,S_p(n) be independent symmetric random walks in Z^d. We establish moderate deviations and law of the iterated logarithm for the intersection of the ranges #{S_1[0,n]\cap... \cap S_p[0,n]} in the case d=2, p\ge 2 and the case…
Based on a law of the iterated logarithm for independent random variables sequences, an iterated logarithm theorem for NA sequences with non-identical distributions is obtained. The proof is based on a Kolmogrov-type exponential inequality.
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
A version of the Law of the Iterated Logarithm for smooth functions in the upper-half space is proved. As a consequence, we show that certain size conditions on the gradient and the gradient of the laplacian of a smooth function, lead to…
In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.
We derive laws of the iterated logarithm for random walks on random conductance models under the assumption that the random walks enjoy long time sub-Gaussian heat kernel estimates.
In this paper, we study the number of moves in a multidimensional elephant random walk with stops. We establish several convergence results for the number of moves, including the law of large numbers and the law of iterated logarithm. Using…
We survey the known and expected properties of the minimal log discrepancy, the local invariant of a log variety.
In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and…
Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of…
In this book chapter we survey known approaches and algorithms to compute discrepancy measures of point sets. After providing an introduction which puts the calculation of discrepancy measures in a more general context, we focus on the…
We develop a new method for showing that a given sequence of random variables verifies an appropriate law of the iterated logarithm. Our tools involve the use of general estimates on multidimensional Wasserstein distances, that are in turn…
Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the large-time…
It was believed that the Mertens function is a simple random walk in the first versions of the article, so its asymptotic behavior obeys the law of the iterated logarithm. In the latest version of the article we show why the asymptotic…
We establish laws of the iterated logarithm for intrinsic volumes of the convex hull of many-step, multidimensional random walks whose increments have two moments and a non-zero drift. Analogous results in the case of zero drift, where the…
We consider the almost sure asymptotic behavior of the periodogram of stationary and ergodic sequences. Under mild conditions we establish that the limsup of the periodogram properly normalized identifies almost surely the spectral density…