Related papers: Extinctions and Correlations for Uniformly Discret…
The full hierarchy of multiple-point correlation functions for diffusion-limited annihilation, A + A -> 0, is obtained analytically and explicitly, following the method of intervals. In the long time asymptotic limit, the correlation…
We impose the uniform probability measure on the set of all discrete Gelfand-Tsetlin patterns of depth $n$ with the particles on row $n$ in deterministic positions. These systems equivalently describe a broad class of random tilings models,…
We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
Given two disjoint sets $W_1$ and $W_2$ of points in the plane, the Optimal Discretization problem asks for the minimum size of a family of horizontal and vertical lines that separate $W_1$ from $W_2$, that is, in every region into which…
We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially non-local and time non-local dependence on the density. Using one-dimensional…
Unique intensity features arising from dynamical diffraction arise in coherent x-ray nanobeam diffraction patterns of crystals having thicknesses larger than the x-ray extinction depth or exhibiting combinations of nanoscale and mesoscale…
We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
We obtain explicit criteria for both exponential ergodicity and strong ergodicity for one-dimensional time-changed symmetric stable processes with $\alpha\in(1,2)$. Explicit lower bounds for ergodic convergence rates are given.
In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical,…
We establish by exact, nonperturbative methods a universality for the correlation functions in Kraichnan's ``rapid-change'' model of a passively advected scalar field. We show that the solutions for separated points in the convective range…
We study the global fluctuations for a class of determinantal point processes coming from large systems of non-colliding processes and non-intersecting paths. Our main assumption is that the point processes are constructed by biorthogonal…
The recent proliferation of correlated percolation models---models where the addition of edges/vertices is no longer independent of other edges/vertices---has been motivated by the quest to find discontinuous percolation transitions. The…
Two-dimensional (2D) spectroscopy provides information about dissipative processes subsequent to electronic excitation, which play a functional role in energy harvesting materials and devices. This technique is particularly sensitive to…
It is shown that a separated sequence of points in the unit disc of the complex plane is in fact uniformly separated, if there exists a certain intermediate sequence whose separated subsequences are uniformly separated. This property is…
We investigate the decay of spatial correlations of $\mathcal{PT}$-symmetric non-Hermitian one-dimensional models that host higher-order exceptional points. Beyond a certain correlation length, they develop anomalous power-law behavior that…
We discuss recent results on decay of correlations for non-uniformly expanding maps. Throughout the discussion, we address the question of why different dynamical systems have different rates of decay of correlations and how this may…
A new method is introduced allowing to solve exactly the reactions A+A->inert and A+A->A on the 1D lattice with synchronous diffusional dynamics (simultaneous hopping of all particles). Exact connections are found relating densities and…