Related papers: A model problem for multiplicative chaos in number…
We develop a new method for constructing approximate decompositions of dense graphs into sparse graphs and apply it to longstanding decomposition problems. For instance, our results imply the following. Let $G$ be a quasi-random $n$-vertex…
By using the Krylov subspace technique to generate the spin coherent states in kicked top model, a prototype model for studying quantum chaos, the accessible system size for studying the Husimi functions of eigenstates can be much larger…
The multidimensional knapsack problem (MKP) is an NP-hard combinatorial optimization problem whose solution is determining a subset of maximum total profit items that do not violate capacity constraints. Due to its hardness, large-scale MKP…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the stochastic process during generation the orbit. A Baire…
We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball…
In the context of mod-Gaussian convergence, as defined previously in our work with J. Jacod, we obtain lower bounds for local probabilities for a sequence of random vectors which are approximately Gaussian with increasing covariance. This…
Using the technology of harmonic analysis, we derive a crossing equation that acts only on the scalar primary operators of any two-dimensional conformal field theory with $U(1)^c$ symmetry. From this crossing equation, we derive bounds on…
We prove multiplier theorems on rank one noncompact symmetric spaces which improve aspects of existing results. A common theme of our main results is that we partially drop specific assumptions on the multiplier function such as a…
We note how several central results in multiplicative number theory may be rephrased naturally in terms of multiplicative functions $f$ that pretend to be another multiplicative function $g$. We formalize a `distance' which gives a measure…
The Riemann Hypothesis (RH) - that all nonreal zeros of Riemann's zeta function shall have real part 1/2 - remains a major open problem. Its most concrete equivalent is that an infinite sequence of real numbers, the Keiper--Li constants,…
The problem of determining the (least) fixpoint of (higher-dimensional) functions over the non-negative reals frequently occurs when dealing with systems endowed with a quantitative semantics. We focus on the situation in which the…
Hyperchaos is distinguished from chaos by the presence of at least two positive Lyapunov exponents instead of just one in dynamical systems. A general scenario is presented here that shows emergence of hyperchaos with a sudden large…
We study cancellation in sums of Hecke eigenvalues over irreducible quadratic polynomials over short intervals. In particular, we look at an average over bases of Hecke forms of weight $k$ in the range $\vert k-K\vert<K^\theta$ where…
Let $1/2\leq\beta<1$, $p$ be a generic prime number and $f_\beta$ be a random multiplicative function supported on the squarefree integers such that $(f_\beta(p))_{p}$ is an i.i.d. sequence of random variables with distribution…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
We show that the Cappell-Shaneson version of Pick's theorem for simple lattice polytopes is a consequence of a general relation between characteristic numbers of virtual submanifolds dual to the characteristic classes of a stably almost…
We characterize a Hawkes point process with kernel proportional to the probability density function of Mittag-Leffler random variables. This kernel decays as a power law with exponent $\beta +1 \in (1,2]$. Several analytical results can be…
Jain's iterative rounding theorem is a well-known result in the area of approximation algorithms and, more broadly, in combinatorial optimization. The theorem asserts that LP relaxations of several problems in network design and…
Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such…