Related papers: Percolation and coarse conformal uniformization
In this paper we study transversely holomorphic foliations of complex codimension one with some hypothesis on the transverse structure.
We show that majorization provides a powerful approach to the coherence conveyed by partially polarized transversal electromagnetic waves. Here we present the formalism, provide some examples and compare with standard measures of…
To a singular foliation on the plane corresponds a circular boundary at infinity endowed with a pre-lamination on the circle. We solve the converse direction. We determine which pre-lamination on the circle are boundary at infinity of a…
In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square,…
We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…
Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density…
Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Moebius strip for different aspect ratios. The asynchronous parallelization of the simulation makes very large system and sample…
A continuum theory of partially fluidized granular flows is developed. The theory is based on a combination of the equations for the flow velocity and shear stresses coupled with the order parameter equation which describes the transition…
We study controlled systems which are uniformly observable and differentially observable with an order larger than the system state dimension. We establish that they may be transformed into a (partial) triangular canonical form but with…
The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…
There exist tilings of the plane with pairwise noncongruent triangles of equal area and bounded perimeter. Analogously, there exist tilings with triangles of equal perimeter, the areas of which are bounded from below by a positive constant.…
In this work, we consider critical planar site percolation on the triangular lattice and derive sharp estimates on the asymptotics of the probability of half-plane $j$-arm events for $j \geq 1$ and planar (polychromatic) $j$-arm events for…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
It is known that similar physical systems can reveal two quite different ways of behavior, either coarsening, which creates a uniform state or a large-scale structure, or formation of ordered or disordered patterns, which are never…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
In a recent article, one of the authors used $c=0$ logarithmic conformal field theory to predict crossing-probability formulas for percolation clusters inside a hexagon with free boundary conditions. In this article, we verify these…
We prove that, with probability 1, all orthogonal projections of the natural measure on a percolation fractal are absolutely continuous and (except for the horizontal and vertical projection) have H\"older continuous density.
Jammed granular media and glasses exhibit spatial long-range correlations as a result of mechanical equilibrium. However, the existence of such correlations in the flowing matter, where the mechanical equilibrium is unattainable, has…
Transverse momentum fluctuations can be understood as resulting from clustering of strings or partons. Data allows to distinguish clustering without percolation, from clustering with percolation. Percolation is clearly favored by data.
We present a conjecture about partitions, with a very elementary formulation.