Related papers: The Harmonic Measure for critical Potts clusters
We study the statistics of the work done on a quantum critical system by quenching a control parameter in the Hamiltonian. We elucidate the relation between the probability distribution of the work and the Loschmidt echo, a quantity…
A Fortuin-Kasteleyn cluster on a torus is said to be of type $\{a,b\}, a,b\in\mathbb Z$, if it possible to draw a curve belonging to the cluster that winds $a$ times around the first cycle of the torus as it winds $-b$ times around the…
The invaded cluster approach is extended to 2D Potts model with annealed vacancies by using the random-cluster representation. Geometrical arguments are used to propose the algorithm which converges to the tricritical point in the…
We report on numerical investigation of fractal properties of critical interfaces in two-dimensional Potts models. Algorithms for finding percolating interfaces of Fortuin-Kasteleyn clusters, their external perimeters and interfaces of spin…
We study properties of the harmonic measure of balls in typical large discrete trees. For a ball of radius $n$ centered at the root, we prove that, although the size of the boundary is of order $n$, most of the harmonic measure is supported…
Due to Fortuin and Kastelyin the $q$ state Potts model has a representation as a sum over random graphs, generalizing the Potts model to arbitrary $q$ is based on this representation. A key element of the Random Cluster representation is…
We construct generalized regular representations of the wreath product of a compact group with the infinite symmetric group. The characters of these representations are determined by probability measures on families of partitions called 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…
We prove that the $q$-state Potts model and the random-cluster model with cluster weight $q>4$ undergo a discontinuous phase transition on the square lattice. More precisely, we show - Existence of multiple infinite-volume measures for the…
Random walkers absorbing on a boundary sample the Harmonic Measure linearly and independently: we discuss how the recurrence times between impacts enable non-linear moments of the measure to be estimated. From this we derive a new technique…
In this paper, we consider feature screening for ultrahigh dimensional clustering analyses. Based on the observation that the marginal distribution of any given feature is a mixture of its conditional distributions in different clusters, we…
This paper deals with random walks on isometry groups of Gromov hyperbolic spaces, and more precisely with the dimension of the harmonic measure $\nu$ associated with such a random walk. We first establish a link of the form $\dim \nu \leq…
We study the discrete Gaussian free field (harmonic crystal) on $\mathbb{Z}^d$, $d\geq 3$, with uniformly elliptic and bounded random conductances sampled according to a sufficiently mixing environment measure. We consider the hard wall…
In this article we investigate a problem within Dempster-Shafer theory where 2**q - 1 pieces of evidence are clustered into q clusters by minimizing a metaconflict function, or equivalently, by minimizing the sum of weight of conflict over…
In this paper we extend the construction of random walks with a prescribed Poisson boundary to the case of measures in the class of a generalized Gibbs state. The price for dropping the $\alpha$-quasiconformal assumptions is that we must…
We consider multidimensional random walks in pyramidal cones (or multidimensional orthants), which are intersections of a finite number of half-spaces. We explore the connection between the existence of (positive) discrete harmonic…
An original experimental method for determining the empirical probability distribution function (PDF) of the quality factor (Q) of a mode-stirred reverberation chamber is presented. Spectral averaging of S-parameters across a relatively…
In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment…
Quantum walks constitute a versatile platform for simulating transport phenomena on discrete graphs including topological material properties while providing a high control over the relevant parameters at the same time. To experimentally…
In this article we are interested in finding positive discrete harmonic functions with Dirichlet conditions in three quadrants. Whereas planar lattice (random) walks in the quadrant have been well studied, the case of walks avoiding a…