منابع مشابه
Introduction 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 کاملMultiple Schramm-Loewner Evolutions and Statistical Mechanics Martingales
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to satisfy this condition leads to some natural processes, which we study in this note. We give examples of such multiple SLEs and discuss how a choice of conform...
متن کاملLectures on Schramm–Loewner Evolution
These notes are based on a course given to Masters students in Cambridge. Their scope is the basic theory of Schramm–Loewner evolution, together with some underlying and related theory for conformal maps and complex Brownian motion. The structure of the notes is influenced by our attempt to make the material accessible to students having a working knowledge of basic martingale theory and Itô ca...
متن کاملRegularity of Schramm-Loewner evolutions, annular crossings, and rough path theory
When studying stochastic processes, it is often fruitful to understand several different notions of regularity. One such notion is the optimal Hölder exponent obtainable under reparametrization. In this paper, we show that chordal SLEκ in the unit disk for κ ≤ 4 can be reparametrized to be Hölder continuous of any order up to 1/(1 + κ/8). From this, we obtain that the Young integral is well def...
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 2009
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.2107