相关论文: Ghost distributions of regular sequences are affin…
The k-regular sequences exhibit a self-similar behaviour between powers of k. One way to study this self-similarity is to attempt to describe the limiting shape of the sequence using measures, which results in an object which we call the…
We extend the existence of ghost measures beyond nonnegative primitive regular sequences to a large class of nonnegative real-valued regular sequences. In the general case, where the ghost measure is not unique, we show that they can be…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
Zaremba's conjecture concerns a formation of continued fraction expansions for rational numbers with partial quotient bounded by an absolute constant. We present asymptotic estimates for the size of $\epsilon$-thickening of certain fractal…
The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…
We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the…
We show that any self-conformal measure $\mu$ on $\mathbb{R}$ is uniformly scaling and generates an ergodic fractal distribution. This generalizes existing results by removing the need for any separation condition. We also obtain…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
We characterize the existence of certain geometric configurations in the fractal percolation limit set $A$ in terms of the almost sure dimension of $A$. Some examples of the configurations we study are: homothetic copies of finite sets,…
Counts of galaxies as a function of apparent magnitude are among the most time-honored observations in cosmology. In this Letter, we focus on some statistical properties of these counts which are fundamental in order to characterize the…
In a previous article, we constructed an entire power series over $p$-adic weight space (the 'ghost series') and conjectured, in the $\Gamma_0(N)$-regular case, that this series encodes the slopes of overconvergent modular forms of any…
We study the distribution of the cokernels of adjacency matrices (the Smith groups) of certain models of random $r$-regular graphs and directed graphs, using recent mixing results of M\'esz\'aros. We explain how convergence of such…
The interest for uniformly distributed (u.d.) sequences of points, in particular for sequences with small discrepancy, arises from various applications. For instance, low-discrepancy sequences, which are sequences with a discrepancy of…
We prove singularity of some distributions of random continued fractions that correspond to iterated function systems with overlap and a parabolic point. These arose while studying the conductance of Galton-Watson trees.
The notion of a phantom distribution function (phdf) was introduced by O'Brien (1987). We show that the existence of a phdf is a quite common phenomenon for stationary weakly dependent sequences. It is proved that any $\alpha$-mixing…
To prove presence of chaos for fractals, a new mathematical concept of abstract similarity is introduced. As an example, the space of symbolic strings on a finite number of symbols is proved to possess the property. Moreover, Sierpinski…
We study the geometric properties of random multiplicative cascade measures defined on self-similar sets. We show that such measures and their projections and sections are almost surely exact-dimensional, generalizing Feng and Hu's result…
We analyze subsamples of Abell and ACO cluster catalogs, in order to study the spatial properties of the large scale matter distribution. The subsamples analyzed are estimated to be nearly complete and are the standard ones used in the…
Ghost imaging is an unconventional imaging technique that generates high resolution images by correlating the intensity of two light beams, neither of which independently contains useful information about the shape of the object. Ghost…
Ghost projection is the reversed process of computational classical ghost imaging that allows any desired image to be synthesized using a linear combination of illuminating patterns. Typically, physical attenuating masks are used to produce…