Geometric Interpretation of Half-Plane Capacity
نویسندگان
چکیده
منابع مشابه
Geometric Interpretation of Half-Plane Capacity
Abstract Schramm-Loewner Evolution describes the scaling limits of interfaces in certain statistical mechanical systems. These interfaces are geometric objects that are not equipped with a canonical parametrization. The standard parametrization of SLE is via half-plane capacity, which is a conformal measure of the size of a set in the reference upper half-plane. This has useful harmonic and com...
متن کاملA Geometric Interpretation of Half-Plane Capacity
Let A be a bounded, relatively closed subset of the upper half plane H whose complement in H is simply connected. If Bt is a standard complex Brownian motion and τA = inf{t ≥ 0 : Bt 6∈ H \A}, the half-plane capacity hcap(A) is defined as hcap(A) := lim y→∞ y E [Im(BτA)] . This quantity arises in the study of Schramm-Loewner Evolutions (SLE). In this note, we show that hcap(A) is comparable to a...
متن کاملThe geometric interpretation of inversion formulae for rational plane curves
Given a faithful parameterization P(t) of a rational plane curve, an inversion formula t = f(x,y) gives the parameter value corresponding to a point (x,y) on the curve, where f is a rational function in x and y. We investigate the relationship between a point (x*, y*) not on the curve and the corresponding point P(t*) on the curve, where t* = f(x*, y*). It is shown that for a rational quadratic...
متن کاملOn the Linear Combinations of Slanted Half-Plane Harmonic Mappings
In this paper, the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.
متن کاملPlane Strain Deformation of a Poroelastic Half-Space Lying Over Another Poroelastic Half-Space
The plane strain deformation of an isotropic, homogeneous, poroelastic medium caused by an inclined line-load is studied using the Biot linearized theory for fluid saturated porous materials. The analytical expressions for the displacements and stresses in the medium are obtained by applying suitable boundary conditions. The solutions are obtained analytically for the limiting case of undrained...
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: Electronic Communications in Probability
سال: 2009
ISSN: 1083-589X
DOI: 10.1214/ecp.v14-1517