Related papers: The Harmonic Measure for critical Potts clusters
In this paper, we focus on Pitman closeness probabilities when the estimators are symmetrically distributed about the unknown parameter $\theta$. We first consider two symmetric estimators $\hat{\theta}_1$ and $\hat{\theta}_2$ and obtain…
We consider importance sampling for estimating the probability that a light-tailed $d$-dimensional random walk exits through one of many disjoint rare-event regions before reaching an anticipated target. This problem arises in sequential…
We propose a new approach for finding discrete harmonic functions in the quarter plane with Dirichlet conditions. It is based on solving functional equations that are satisfied by the generating functions of the values taken by the harmonic…
Computing the marginal likelihood (also called the Bayesian model evidence) is an important task in Bayesian model selection, providing a principled quantitative way to compare models. The learned harmonic mean estimator solves the…
Circular-harmonic spectra are a compact representation of local image features in two dimensions. It is well known that the computational complexity of such transforms is greatly reduced when polar separability is exploited in steerable…
Especially in lattice structured populations, homogeneous mixing represents an inadequate assumption. Various improvements upon the ordinary pair approximation based on a number of assumptions concerning the higher-order correlations have…
In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when…
We propose a new model of cluster growth according to which the probability that a new unit is placed in a point at a distance $r$ from the city center is a Gaussian with mean equal to the cluster radius and variance proportional to the…
Analytic formulas to calculate statistical uncertainties of $v_{n}\{2k\}$ harmonics extracted from the Q-cumulants are presented. The Q-cumulants are multivariate polynomial functions of the weighted means of $2m$-particle azimuthal…
We show that observing the trajectories of confined particles in a thermal equilibrium state yields an estimate on the free-space diffusion coefficient. For generic trapping potentials and interactions between particles, the estimate comes…
We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be…
We study a 2-parametric family of probability measures on an infinite-dimensional simplex (the Thoma simplex). These measures originate in harmonic analysis on the infinite symmetric group (S.Kerov, G.Olshanski and A.Vershik, Comptes Rendus…
A geometric approach to critical fluctuations of a nonequilibrium model is reported. The two-dimensional majority vote model was investigated by Monte Carlo simulations on square lattices of various sizes and a detailed scaling analysis of…
A closed equilateral random walk in 3-space is a selection of unit length vectors giving the steps of the walk conditioned on the assumption that the sum of the vectors is zero. The sample space of such walks with $n$ edges is the…
We consider the scaling limit of the two-dimensional $q$-state Potts model for $q\leq 4$. We use the exact scattering theory proposed by Chim and Zamolodchikov to determine the one and two-kink form factors of the energy, order and disorder…
A quantum ensemble $\{(p_x, \rho_x)\}$ is a set of quantum states each occurring randomly with a given probability. Quantum ensembles are necessary to describe situations with incomplete a priori information, such as the output of a…
A harmonic mapping is a univalent harmonic function of one complex variable. We define a family of harmonic mappings on the unit disk whose images are rotationally symmetric rosettes with $n$ cusps or n nodes, where $n \ge 3$. These…
First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods. These methods necessarily fix one of these two…
We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the…
A cluster mean-field method is introduced and the applications to the Ising and Heisenberg models are demonstrated. We divide the lattice sites into clusters whose size and shape are selected so that the equivalence of all sites in a…