Related papers: Hard rods: statistics of parking configurations
Consider the Delaunay triangulation T of a set P of points in the plane as a Euclidean graph, in which the weight of every edge is its length. It has long been conjectured that the dilation in T of any pair p, p \in P, which is the ratio of…
A parking function is a sequence $(a_1,\dots, a_n)$ of positive integers such that if $b_1\leq\cdots\leq b_n$ is the increasing rearrangement of $a_1,\dots,a_n$, then $b_i\leq i$ for $1\leq i\leq n$. In this paper we obtain some new results…
We show that correlation functions have to satisfy contraint relations, owing to the non-negativity of the power spectrum of the underlying random process. Specifically, for any statistically homogeneous and (for more than one spatial…
A self-consistent mode-coupling theory is presented for the viscosity of solutions of charged rod-like polymers. The static structure factor used in the theory is obtained from polymer integral equation theory; the Debye-H\"{u}ckel…
For a one-dimensional model in which the two-body interactions are long-range and strong, the system almost crystallizes. The harmonic modes of such a lattice can be used to compute the ground state wave function and the dynamical…
Benjamini, Kalai and Schramm showed that a monotone function $f : \{-1,1\}^n \to \{-1,1\}$ is noise stable if and only if it is correlated with a half-space (a set of the form $\{x: \langle x, a\rangle \le b\}$). We study noise stability in…
Based on the Sloan Digital Sky Survey DR6 (SDSS) and Millennium Simulation (MS) we investigate the alignment between galaxies and large-scale structure. For this purpose we develop two new statistical tools, namely the alignment correlation…
We derive exact density functionals for systems of hard rods with first-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The…
We introduce a new paradigm for finite and infinite strict-one-dimensional uniform electron gases. In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. In the high-density limit (small-$r_s$, where…
In this paper, we mainly study two notions of pattern avoidance in parking functions. First, for any collection of length 3 patterns, we compute the number of parking functions of size $n$ that avoid them under the first notion. This is…
We give a short and elementary proof of stability for strong solutions of the spatially homogeneous Landau equation with Coulomb collisions, measured in relative entropy. The argument yields an explicit differential inequality for relative…
We consider two variations of the discrete car parking problem where at every vertex of the integers a car arrives with rate one, now allowing for parking in two lines. a) The car parks in the first line whenever the vertex and all of its…
We prove the \textbf{NP}-hardness, using Karp reductions, of some problems related to the correlation polytope and its corresponding cone, spanned by all of the $n\times n$ rank-one matrices over $\{0,1\}$. The problems are: membership,…
We derive a local approximation for the correlation energy in two-dimensional electronic systems. In the derivation we follow the scheme originally developed by Colle and Salvetti for three dimensions, and consider a Gaussian approximation…
We investigate the long-time behavior of weak solutions to the thin-film type equation $$v_t =(xv - vv_{xxx})_x\ ,$$ which arises in the Hele-Shaw problem. We estimate the rate of convergence of solutions to the Smyth-Hill equilibrium…
Results of a previous article with the same title are retrieved by a different method. A one-component plasma is bounded by a plane surface. The plasma is fully coupled to the electromagnetic field, therefore the charge correlations are…
We study the mass density distribution of Newtonian self-gravitating systems. Modeling the system as a fluid in hydrostatical equilibrium, we obtain from first principle the field equation and its solution of correlation function $\xi(r)$…
We study the equilibrium correlation function of the polaron-dressed tunnelling operator in the dissipative two-state system and compare the asymptoptic dynamics with that of the position correlations. For an Ohmic spectral density with the…
We study the clustering properties of the recently compiled HIPASS neutral hydrogen (HI) sources catalogue using the two point correlation function in redshift space. If the two point correlation is modelled as a power law,…
The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte…