The blanket time of a random walk on a graph G is the expected time until the proportion of time spent at each vertex approximates the stationary distribution. In 1996, Winkler and Zuckerman conjectured that the blanket time is of the same order as the cover time. Ding, Lee and Peres proved this conjecture in 2010 by relating both terms to the maximum of the Gaussian free field on G. We outline...

The V -algebras are the non-local matrix generalization of the well-known W -algebras. Their classical realizations are given by the second Poisson brackets associated with the matrix pseudodifferential operators. In this paper, by using the general Miura transformation, we give the decomposition theorems for the second Poisson brackets, from which we are able to construct the free field realiz...

An approach to systematically implement open-closed string duality for free large N gauge theories is summarised. We show how the relevant closed string moduli space emerges from a reorganisation of the Feynman diagrams contributing to free field correlators. We also indicate why the resulting integrand on moduli space has the right features to be that of a string theory on AdS.

We investigate strategies for field-free three dimensional molecular axis alignment using strong nonresonant laser fields under experimentally realistic conditions. Using the polarizabilites and rotational constants of an asymmetric top rotor molecule (ethene, C2H4), we consider three different methods for axis alignment of a Boltzmann distribution of rotors at 4 K. Specifically, we compare the...

We define a scaling limit of the height function on the domino tiling model (dimer model) on simplyconnected regions in Z and show that it is the “massless free field”, a Gaussian process with independent coefficients when expanded in the eigenbasis of the Laplacian. Résumé On définit une “limite d’échelle” pour la fonction d’hauteur dans le modèle des dimères dans Z. Nous montrons que la limit...

After reviewing some aspects of Cohn’s theory of the free field, we give another proof of a theorem of Lewin: the subfield of rational elements in the field of Malcev-Neumann series on the free group is isomorphic to the free field.

Phase-field models are very attractive in view of their numerical simplicity. With only a few lines of code, one can model complex physical situations such as dendritic growth. From this point of view, they constitute very interesting tools for teaching purposes at graduate level. The main difficulty with these models is in their formulation, which incorporates the physical ingredients in a sub...

The d − dimensional Gaussian free field (GFF) is a natural d − dimensional dimensional time analog of Brownian motion. It places an important role in statistical physics and the theory of random surfaces. This term paper will focus on the case where d = 2. Let D ⊂ C be a bounded domain with smooth boundary and C∞ 0 (D) denote the set of smooth functions compactly supported in D. The Dirichlet i...

A scattering description is proposed for a boundary perturbation of a c = 1 SL(2, Z) invariant conformal field theory. The bulk massless S-matrices are of the form of Zamolodchikov’s staircase model. Using the boundary version of the thermodynamic Bethe ansatz, we show that the boundary free energy goes through a series of integer valued plateaux as a function of system size. Typeset using REVTEX

In this section we will consider the general properties of the solution p(r, t) of the Smoluchowski equation in the case that the force field is derived from a potential, i.e., F (r) = −∇U(r) and that the potential is finite everywhere in the diffusion doamain Ω. We will demonstrate first that the solutions, in case of reaction-free boundary conditions, obey an extremum principle, namely, that ...