Related papers: A Coupling, and the Darling-Erdos Conjectures
We consider a multi-particle generalization of linear edge-reinforced random walk (ERRW). We observe that in absence of exchangeability, new techniques are needed in order to study the multi-particle model. We describe an unusual coupling…
This Letter proposes a controlled coupling process for information processing. The net effect of conventional coupling is isolated from the dynamical system and is analyzed in depth. The stability of the process is studied. We show that the…
Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the…
We show that the comment [arXiv:1104.0697] by Levin and Pakter on our work [arXiv:1008.1421] is conceptually unfounded, contains misleading interpretations, and is based on results of questionable applicability. We initially provide…
We rigorously derive the Ornstein-Zernike asymptotics of the pair-correlation functions for finite-range Ising ferromagnets in any dimensions and at any temperature above critical.
Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\ binary vectors,…
We provide empirical evidence for the Erd\H{o}s-Straus conjecture by improving computational bounds to $10^{18}$ and by evaluating the solution-counting function $f(p)$ for this conjecture.
The entanglement of superpositions [Phys. Rev. Lett. 97, 100502 (2006)] is generalized to the multipartite scenario: an upper bound to the multipartite entanglement of a superposition is given in terms of the entanglement of the superposed…
We consider the asymptotic behavior of the expectation of the maximum for a special assignment process with constant or i.i.d. coefficients. We show how it depends on the coefficients' distribution.
We identify generic protocols achieving optimal power extraction from a single active particle subject to continuous feedback control under the assumption that its spatial trajectory, but not its instantaneous self-propulsion force, is…
In this article we consider a toy example of an optimal stopping problem driven by fragmentation processes. We show that one can work with the concept of stopping lines to formulate the notion of an optimal stopping problem and moreover, to…
We develop the (co)homological tools that make effective the construction of the quaternionic Darmon points introduced by Matthew Greenberg. In addition, we use the overconvergent cohomology techniques of Pollack--Pollack to allow for the…
A global quantum quench can be modeled by a quantum circuit with local unitary gates. In general, entanglement grows linearly at a rate given by entanglement velocity, which is upper bounded by the growth of the light cone. We show that the…
We consider the parametric estimation of the Ornstein-Uhlenbeck process driven by a non-Gaussian $\alpha$-stable L\'{e}vy process with the stable index $\alpha>1$ and possibly skewed jumps, based on a discrete-time sample over a fixed…
We introduce a class of maximum-entropy states that naturally includes within it all of the major continuous-time stochastic processes that have been applied to animal movement, including Brownian motion, Ornstein-Uhlenbeck motion,…
In 1959 Fejes T\'oth posed a conjecture that the sum of pairwise non-obtuse angles between $N$ unit vectors in $\mathbb S^d$ is maximized by periodically repeated elements of the standard orthonormal basis. We obtain new improved upper…
This paper concerns a long-standing problem raised by Beurling and Wintner on completeness of the dilation system $\{\varphi(kx):k=1,2,\cdots\}$ generated by the odd periodic extension on $\mathbb{R}$ of any $\varphi\in L^2[0,1]$. Up to now…
Several realistic spin-orbital models for transition metal oxides go beyond the classical expectations and could be understood only by employing the quantum entanglement. Experiments on these materials confirm that spin-orbital entanglement…
For the Moran model with strong or moderately strong selection we prove that the fluctuations around the deterministic limit of the line counting process of the ancestral selection graph converge to an Ornstein-Uhlenbeck process. To this…
We consider the fractional Ornstein-Uhlenbeck process with an unknown drift parameter and known Hurst parameter $H$. We propose a new method to test the hypothesis of the sign of the parameter and prove the consistency of the test. Contrary…