Exact Solutions for Loewner Evolutions
نویسندگان
چکیده
منابع مشابه
Exact Solutions for Loewner Evolutions
In this note, we solve the Loewner equation in the upper halfplane with forcing function ξ(t), for the cases in which ξ(t) has a power-law dependence on time with powers 0, 1/2 and 1. In the first case the trace of singularities is a line perpendicular to the real axis. In the second case the trace of singularities can do three things. If ξ(t) = 2 √ κt, the trace is a straight line set at an an...
متن کاملIntroduction to Schramm–Loewner evolutions
we mean an equivalence class of paths modulo reparametrizations. Write CD for the set of chords in D. Given a path γ, we write [γ] for the associated chord; more generally, if γ is a continuous map from any compact subinterval I of [0,∞] to Û , starting at z0 and ending at z1, we can obtain a chord [γ] in D by choosing an increasing homeomorphism φ : [0, 1] → I and setting [γ] = [γ ◦ φ]. Write ...
متن کاملOn Multiple Schramm-Loewner Evolutions
In this note we consider the ansatz for Multiple Schramm-Loewner Evolutions (SLEs) proposed by Bauer, Bernard and Kytölä from a more probabilistic point of view. Here we show their ansatz is a consequence of conformal invariance, reparameterisation invariance and a notion of absolute continuity. In so doing we demonstrate that it is only consistent to grow multiple SLEs if their κ parameters ar...
متن کاملConformal Field Theories in Random Domains and Stochastic Loewner Evolutions
where L is the number of links of the lattice, NC the number of clusters in the configuration C and ‖C‖ the number of links inside the NC clusters, usually called FK-clusters. Criticality is then encoded in the fractal nature of these clusters. The stochastic Loewner evolutions (SLE) [2] are mathematically well-defined processes describing the growth of random sets, called the SLE hulls, and of...
متن کاملConformal Field Theories of Stochastic Loewner Evolutions . [ CFTs of SLEs ]
Stochastic Loewner evolutions (SLEκ) are random growth processes of sets, called hulls, embedded in the two dimensional upper half plane. We elaborate and develop a relation between SLEκ evolutions and conformal field theories (CFT) which is based on a group theoretical formulation of SLEκ processes and on the identification of the proper hull boundary states. This allows us to define an infini...
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2004
ISSN: 0022-4715
DOI: 10.1023/b:joss.0000022380.93241.24