相关论文: Sharp asymptotics of correlation functions in the …

This paper considers non-negative integer-valued autoregressive processes where the autoregression parameter is close to unity. We consider the asymptotics of this `near unit root' situation. The local asymptotic structure of the likelihood…

We discuss a new approach to data clustering. We find that maximum likelihood leads naturally to an Hamiltonian of Potts variables which depends on the correlation matrix and whose low temperature behavior describes the correlation…

This paper studies networks where all nodes are distributed on a unit square $A\triangleq[(-1/2,1/2)^{2}$ following a Poisson distribution with known density $\rho$ and a pair of nodes separated by an Euclidean distance $x$ are directly…

We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…

In dealing with asymptotic approximation of possibly divergent nets of probability distributions, we are led to study uniform structures on the set of distributions. This paper identifies a class of such uniform structures that may be…

We give an exact formula for the value of the derivative at zero of the gap probability in finite n x n Gaussian ensembles. As n goes to infinity our computation provides an asymptotic (with an explicit constant) of the order n^(1/2). As a…

Exact integral expressions of the skew orthogonal polynomials involved in Orthogonal (beta=1) and Symplectic (beta=4) random matrix ensembles are obtained: the (even rank) skew orthogonal polynomials are average characteristic polynomials…

We propose a highly efficient "worm" like cluster Monte Carlo algorithm for the quantum rotor model in the link-current representation. We explicitly prove detailed balance for the new algorithm even in the presence of disorder. For the…

We consider random q-state Potts models for $3\le q \le 8$ on the square lattice where the ferromagnetic couplings take two values $J_1>J_2$ with equal probabilities. For any q the model exhibits a continuous phase transition both in the…

We consider three models (elliptic, flat and hyperbolic) of Gaussian random analytic functions distinguished by invariance of their zeroes distribution. Asymptotic normality is proven for smooth functionals (linear statistics) of the set of…

We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…

We consider a new formulation of the stochastic coupled cluster method in terms of the similarity transformed Hamiltonian. We show that improvement in the granularity with which the wavefunction is represented results in a reduction in the…

Inspired by the multicanonical approach to simulations of first-order phase transitions we propose for $q$-state Potts models a combination of cluster updates with reweighting of the bond configurations in the…

Universal dimensionless quantities, such as Binder ratios and wrapping probabilities, play an important role in the study of critical phenomena. We study the finite-size scaling behavior of the wrapping probability for the Potts model in…

Let $\mu$ be a measure that samples a subset of a finite ground set, and let $\mathcal{A}_e$ be the event that element $e$ is sampled. The measure $\mu$ is negatively correlated if for any pair of elements $e, f$ one has $\mu(\mathcal{A}_e…

We discuss a new approach to data clustering. We find that maximum likelyhood leads naturally to an Hamiltonian of Potts variables which depends on the correlation matrix and whose low temperature behavior describes the correlation…

We use the cluster method to enumerate permutations avoiding consecutive patterns. We reprove and generalize in a unified way several known results and obtain new ones, including some patterns of length 4 and 5, as well as some infinite…

In the realm of Boltzmann-Gibbs statistical mechanics there are three well known isomorphic connections with random geometry, namely (i) the Kasteleyn-Fortuin theorem which connects the $\lambda \to 1$ limit of the $\lambda$-state Potts…

Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$ \lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B, $$ with…

We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…