Related papers: Correlation function of the Schur process with a f…

We study the $t$-Schur measure on partitions, defined by $ \mathbb{P}(\lambda)=Z^{-1}S_\lambda(x;t)s_\lambda(y) $, where $S_\lambda(x;t)$ denotes the $t$-Schur symmetric functions and $s_\lambda(y)$ the ordinary Schur functions, and $Z$ is…

We propose the finite-size scaling of correlation function in a finite system near its critical point. At a distance ${\bf r}$ in the finite system with size $L$, the correlation function can be written as the product of $|{\bf…

The evolution of granular shear flow is investigated as a function of height in a split-bottom Couette cell. Using particle tracking, magnetic-resonance imaging, and large-scale simulations we find a transition in the nature of the shear as…

The dynamical evolution of small systems undergoing a chiral symmetry breaking transition in the course of rapid expansion is discussed. The time evolution of the dynamical correlation length for trajectories passing through a second-order…

We consider relations with no order on their attributes as in Database Theory. An independent partition of the set of attributes S of a finite relation R is any partition X of S such that the join of the projections of R over the elements…

We consider a particle system of the squared Bessel processes with index $\nu > -1$ conditioned never to collide with each other, in which if $-1 < \nu < 0$ the origin is assumed to be reflecting. When the number of particles is finite, we…

We study the finite-size scaling (FSS) property of the correlation ratio, the ratio of the correlation functions with different distances. It is shown that the correlation ratio is a good estimator to determine the critical point of the…

We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger…

A discrete Gelfand-Tsetlin pattern is a configuration of particles in Z^2. The particles are arranged in a finite number of consecutive rows, numbered from the bottom. There is one particle on the first row, two particles on the second row,…

We derive a product rule satisfied by restricted Schur polynomials. We focus mostly on the case that the restricted Schur polynomial is built using two matrices, although our analysis easily extends to more than two matrices. This product…

As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant…

We use the Unruh effect to analyze the dynamics of classical and quantum correlations for a two-qubit system when one of them is uniformly accelerated for a finite amount of proper time. We show that the quantum correlation is completely…

We give simple linear algebraic proofs of Eynard-Mehta theorem, Okounkov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also discuss certain general properties of the spaces of…

Schur-Weyl duality is a fundamental framework in combinatorial representation theory. It intimately relates the irreducible representations of a group to the irreducible representations of its centralizer algebra. We investigate the analog…

We study the exchange and correlation hole of the valence shell of second row atoms using variational Monte Carlo techniques, especially correlated estimates, and norm-conserving pseudopotentials. The well-known scaling of the valence shell…

The quantum correlations of $N$ noninteracting spinless fermions in their ground state can be expressed in terms of a two-point function called the kernel. Here we develop a general and compact method for computing the kernel in a general…

A certain kernel (sometimes called the Pick kernel) associated to Schur functions on the disk is always positive semi-definite. A generalization of this fact is well-known for Schur functions on the polydisk. In this article, we show that…

We study the linear response of interacting active Brownian particles in an external potential to simple shear flow. Using a path integral approach, we derive the linear response of any state observable to initiating shear in terms of…

In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty). The main result is the computation of the…

While studying the continual gravitational collapse of a massive matter cloud in general relativity towards examining collapse final states, an important issue is that of whether shell-crossing singularities can develop as the collapse…