The Existence of Pair Potential Corresponding to Specified Density and Pair Correlation

Given a potential of pair interaction and a value of activity, one can consider the Gibbs distribution in a finite domain $\Lambda \subset \mathbb{Z}^d$. It is well known that for small values of activity there exist the infinite volume ($\Lambda \to \mathbb{Z}^d$) limiting Gibbs distribution and the infinite volume correlation functions. In this paper we consider the converse problem - we show that given $\rho_1$ and $\rho_2(x)$, where $\rho_1$ is a constant and $\rho_2(x)$ is a function on $\mathbb{Z}^d$, which are sufficiently small, there exist a pair potential and a value of activity, for which $\rho_1$ is the density and $\rho_2(x)$ is the pair correlation function

Tagged particle process in continuum with singular interactions

By using Dirichlet form techniques we construct the dynamics of a tagged particle in an infinite particle environment of interacting particles for a large class of interaction potentials. In particular, we can treat interaction potentials having a singularity at the origin, non-trivial negative part and infinite range, as e.g., the Lennard-Jones potential.Comment: 27 pages, proof for conservativity added, tightened presentatio

Mapping Mutual Fund Investor Characteristics and Modeling Switching Behavior

Securing a mutual fund that meets investment goals is an important reason why some investors exclusively stay with a particular mutual fund and others switch funds within their fund family. This paper empirically investigates investor attitudes toward mutual funds. Our model, based on investor responses, develops an investor\u27s risk profile variable. Results indicate that regardless of whether the investors invest in nonemployer plans or in both employer and nonemployer plans, they consider their investment risk, fund performance, investment mix, and the capital base of the fund before switching funds. The model developed in this study can also assist in predicting investors\u27 switching behavior

Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit

Let $\Gamma$ denote the space of all locally finite subsets (configurations) in $\mathbb R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\Gamma$ in which pairs of particles simultaneously hop over $\mathbb R^d$. We discuss a non-equilibrium dynamics of binary jumps. We prove the existence of an evolution of correlation functions on a finite time interval. We also show that a Vlasov-type mesoscopic scaling for such a dynamics leads to a generalized Boltzmann non-linear equation for the particle density

Temperature correlators in the two-component one-dimensional gas

The quantum nonrelativistic two-component Bose and Fermi gases with the infinitely strong point-like coupling between particles in one space dimension are considered. Time and temperature dependent correlation functions are represented in the thermodynamic limit as Fredholm determinants of integrable linear integral operators.Comment: 40 pages, LaTeX, a4.st

Canada’s Fair Elections Act risks disenfranchising voters and handing an advantage to wealthy candidates

The Canadian government has proposed new legislation to reform electoral law in areas such as voter identification, fraud and campaign finance. The reforms have provoked a fierce reaction, with over 150 political scientists signing a letter of protest. In this post Patti Tamara Lenard summarises the proposals and explains why she and other experts believe they will undermine the integrity of elections in Canada

Markov evolutions and hierarchical equations in the continuum I. One-component systems

General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General considerations are illustrated in a number of concrete examples of Markov evolutions appearing in applications.Comment: 47 page