Related papers: Conformal restriction: The trichordal case
We develop a version of dipolar conformal field theory based on the central charge modification of the Gaussian free field with the Dirichlet boundary condition and prove that correlators of certain family of fields in this theory are…
A nontrivial trigonometric limit of the three-coloring statistical model with the domain wall boundary conditions is considered. In this limit the functional equations, constructed in the previous paper, are solved and a new determinant…
A randomised trapezoidal quadrature rule is proposed for continuous functions which enjoys less regularity than commonly required. Indeed, we consider functions in some fractional Sobolev space. Various error bounds for this randomised rule…
We establish a one-to-one correspondence between K\"ahler metrics in a given conformal class and parallel sections of a certain vector bundle with conformally invariant connection, where the parallel sections satisfy a set of non--linear…
We provide evidence for the existence of non-trivial unitary conformal boundary conditions for a three-dimensional free scalar field, which can be obtained via a coupling to the m'th unitary diagonal minimal model. For large m we can…
We construct continuously parametrised families of conformally invariant boundary operators on densities. These may also be viewed as conformally covariant boundary operators on functions and generalise to higher orders the first-order…
In some recent work, fractal curvatures C^f_k(F) and fractal curvature measures C^f_k(F, .), k = 0, ..., d, have been determined for all self-similar sets F in R^d, for which the parallel neighborhoods satisfy a certain regularity condition…
The central topic of this thesis is two dimensional Quantum Gravity and its properties. The term Quantum Gravity itself is ambiguous as there are many proposals for its correct formulation and none of them have been verified experimentally.…
We calculate Wilson loops in lowest order of perturbation theory for triangular contours whose edges are circular arcs. Based on a suitable disentanglement of the relations between metrical and conformal parameters of the contours, the…
The seminal work of Sheffield showed that when random surfaces called Liouville quantum gravity (LQG) are conformally welded, the resulting interface is Schramm-Loewner evolution (SLE). This has been proved for a variety of configurations,…
We exploit the properties of the three-dimensional hyperbolic space to discuss a simplicial setting for open/closed string duality based on (random) Regge triangulations decorated with null twistorial fields. We explicitly show that the…
Self-similar curves are a recurring motif in nature. The tension-free stationary states of conformally invariant energies describe the simplest curves of this form. Planar logarithmic spirals, for example, are associated with conformal…
We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…
Bond percolation on Cayley graphs provides examples of random graphs. Other examples arise from the dynamical study of proper repetitive subgraphs of Cayley graphs. In this paper we demonstrate that these two families have mutually singular…
We consider infinite conformal iterated function systems on $\mathbb{R}^d$. We study the geometric structure of the limit set of such systems. Suppose this limit set intersects some $l$-dimensional $C^1$-submanifold with positive Hausdorff…
This paper first studies the regularity of conformal homeomorphisms on smooth locally embeddable strongly pseudoconvex CR manifolds. Then moduli of curve families are used to estimate the maximal dilatations of quasiconformal…
This is an introductory account of the emergence of conformal invariance in the scaling limit of planar critical percolation. We give an exposition of Smirnov's theorem (2001) on the conformal invariance of crossing probabilities in site…
We review some of the results that have been derived in the last years on conformal invariance, scaling limits and properties of some two-dimensional random curves. In particular, we describe the intuitive ideas that lead to the definition…
We provide five examples of conformal geometries which are naturally associated with ordinary differential equations (ODEs). The first example describes a one-to-one correspondence between the Wuenschmann class of 3rd order ODEs considered…
In this paper we study the constraints imposed by conformal invariance on extended objects a.k.a defects in a conformal field theory. We identify a particularly nice class of defects that is closed under conformal transformations.…