Harmonic Measure and Winding of Conformally Invariant Curves
نویسندگان
چکیده
منابع مشابه
Harmonic measure and winding of conformally invariant curves.
The exact joint multifractal distribution for the scaling and winding of the electrostatic potential lines near any conformally invariant scaling curve is derived in two dimensions. Its spectrum f(alpha,lambda) gives the Hausdorff dimension of the points where the potential scales with distance r as H approximately r(alpha) while the curve logarithmically spirals with a rotation angle phi=lambd...
متن کاملInverse turbulent cascades and conformally invariant curves.
We offer a new example of conformal invariance (local scale invariance) far from equilibrium-the inverse cascade of surface quasigeostrophic (SQG) turbulence. We show that temperature isolines are statistically equivalent to curves that can be mapped into a one-dimensional Brownian walk (called Schramm-Loewner evolution or SLEkappa). The diffusivity is close to kappa=4, that is, isotemperature ...
متن کاملCritical curves in conformally invariant statistical systems
We consider critical curves — conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit ...
متن کاملStatistics of harmonic measure and winding of critical curves from conformal field theory
Fractal geometry of random curves appearing in the scaling limit of critical two-dimensional statistical systems is characterized by their harmonic measure and winding angle. The former is the measure of the jaggedness of the curves while the latter quantifies their tendency to form logarithmic spirals. We show how these characteristics are related to local operators of conformal field theory a...
متن کاملThe Conformally Invariant Measure on Self-avoiding Loops
The aim of the present paper is to construct and describe a natural measure on the set of self-avoiding loops in the plane and on any Riemann surface. By a self-avoiding loop on a surface S, we mean a continuous injective map from the unit circle into S modulo monotone reparametrizations (i.e. we look only at the trace of the loop and forget about its parametrization). We will construct a measu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2002
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.89.264101