Related papers: Simple CLE in Doubly Connected Domains
We study numerically the fractal dimensions and the bulk three-point connectivity for the spin clusters of the Q-state Potts model in two dimensions with $1\leq Q\leq 4$. We check that the usually invoked correspondence between FK clusters…
A spherical $L$-code, where $L \subseteq [-1,\infty)$, consists of unit vectors in $\mathbb{R}^d$ whose pairwise inner products are contained in $L$. Determining the maximum cardinality $N_L(d)$ of an $L$-code in $\mathbb{R}^d$ is a…
In this paper, we have developed a unitary variant of a double exponential coupled cluster theory, which is capable of mimicking the effects of connected excitations of arbitrarily high rank, using only rank-one and rank-two parametrization…
We consider the problem of finding embeddings of arc-like continua in the plane for which each point in a given subset is accessible. We establish that, under certain conditions on an inverse system of arcs, there exists a plane embedding…
The light cone OPE limit provides a significant amount of information regarding the conformal field theory (CFT), like the high-low temperature limit of the partition function. We started with the light cone bootstrap in the {\it general}…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
We study non-compact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe…
SLE(kappa,rho) is a generalisation of Schramm-Loewner evolution which describes planar curves which are statistically self-similar but not conformally invariant in the strict sense. We show that, in the context of boundary conformal field…
We provide a new construction of the Brownian disks, which have been defined by Bettinelli and Miermont as scaling limits of quadrangulations with a boundary when the boundary size tends to infinity. Our method is very similar to the…
A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds which were proposed in the last decades. Such an operation is indispensable in order to perform…
We introduce constellation ensembles, in which charged particles on a line (or circle) are linked with charged particles on parallel lines (or concentric circles). We present formulas for the partition functions of these ensembles in terms…
For every partial combinatory algebra (pca), we define a hierarchy of extensionality relations using ordinals. We investigate the closure ordinals of pca's, i.e. the smallest ordinals where these relations become equal. We show that the…
We present a new code, named COCAL - Compact Object CALculator, for the computation of equilibriums and quasiequilibrium initial data sets of single or binary compact objects of all kinds. In the cocal code, those solutions are calculated…
We construct a sequence of compact embedded minimal disks in a ball in Euclidean 3-space, whose boundaries lie in the boundary of the ball, such that the curvature blows up only at a prescribed discrete (and hence, finite) set of points on…
This thesis studies skein relations in cluster algebras arising from punctured surfaces. We introduce skein-type identities expressing cluster variables associated with incompatible curves on a surface in terms of cluster variables…
Molecular simulations of the self-assembly of cone-shaped particles with specific, attractive interactions are performed. Upon cooling from random initial conditions, we find that the cones self assemble into clusters and that clusters…
We study the commutation relation for 2-radial SLE in the unit disc starting from two boundary points. We follow the framework introduced by Dub\'{e}dat. Under an additional requirement of the interchangeability of the two curves, we…
The peanosphere (or "mating of trees") construction of Duplantier, Miller, and Sheffield encodes certain types of $\gamma$-Liouville quantum gravity (LQG) surfaces ($\gamma \in (0,2)$) decorated with an independent SLE$_{\kappa}$ ($\kappa =…
We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites…
Let $A \subset \mathbb{R} ^2 $ be a smooth doubly connected domain. We consider the Dirichlet energy $E(u)=\int_{A} |\nabla u|^2$, where $u:A \rightarrow \mathbb{C}$, and look for critical points of this energy with prescribed modulus…