Now showing items 1-10 of 46
The Martin boundary in non-Lipschitz domains
(American Mathematical Society, 1993)
The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean boundary in C [to the power of gamma] domains, where [gamma](x) = bx log log(1/x)/ log log log(1/x), b small. A counterexample shows that this result is very nearly sharp.
Intersection local time for points of infinite multiplicity
(Institute of Mathematical Statistics, 1994-04)
For each a [is an element of the set] (0, 1/2), there exists a random measure [beta] [subscript] a which is supported on the set of points where two-dimensional Brownian motion spends a units of local time. The measure [beta] [subscript] a is carried by a set which has Hausdorff dimension equal to 2−a. A Palm measure ...
Diffusion on curved, periodic surfaces
(American Physical Society, 1999-07)
We present a simulation algorithm for a diffusion on a curved surface given by the equation [omega](r)50. The algorithm is tested against analytical results known for diffusion on a cylinder and a sphere, and applied to the diffusion on the P, D, and G periodic nodal surfaces. It should find application in an interpretation ...
On minimal parabolic functions and time-homogenous parabolic h-transforms
(American Mathematical Society, 1999-03-29)
Does a minimal harmonic function h remain minimal when it is viewed as a parabolic function? The question is answered for a class of long thin semi-infinite tubes D [is an element of the subset of real numbers to the power of] d of variable width and minimal harmonic functions h corresponding to the boundary point of D "at ...
A counterexample to the "hot spots" conjecture
(Princeton University and Institute for Advanced Study, 1999-01)
We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with Neumann boundary conditions is simple and such that the corresponding eigenfunction attains its strict maximum at an interior point ...
The level sets of iterated Brownian motion
We show that the Hausdorff dimension of every level set of iterated Brownian motion is equal to 3/4.
The boundary Harnack principle for non-divergence form elliptic operators
(Cambridge University Press, 1994)
If L is a uniformly elliptic operator in non–divergence form, the boundary Harnack principle for the ratio of positive L–harmonic functions holds in Hölder domains of order [alpha] if [alpha] > 1/2. A counterexample shows that 1/2 is sharp. For Hölder domains of order [alpha] with [alpha is an element of the set] (0, 1], the ...
2-D Brownian motion in a system of traps: Application of conformal transformations
(Institute of Physics, 1992)
We study two-dimensional Brownian motion in a periodic system of traps using conformal transformations. The system is periodic in the x and y directions. We calculate the ratio of the drift along the y-axis to the drift along the x-axis. The drift of the Brownian particle is induced by conditioning and by the asymmetry of the ...
A three-dimensional Brownian path reflected on a Brownian path is a free Brownian path
(Springer Science+Business Media B.V., 1993)
Three-dimensional Brownian path reflected on Brownian path is a free Brownian path.
Hölder domains and the boundary Harnack principle
(Duke University Press, 1991-10)
A version of the boundary Harnack principle is proven.