Now showing items 1-10 of 84
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.
Reduction of dimensionality in a diffusion search process and kinetics of gene expression
(North-Holland (Elsevier), 2000-03-01)
In order to activate a gene in a DNA molecule a specific protein (transcription factor) has to bind to the promoter of the gene. We formulate and partially answer the following question: how much time does a transcription factor, which activates a given gene, need in order to find this gene inside the nucleus of a cell? The ...
Super-Brownian motion with reflecting historical paths
(Springer-Verlag GmbH, 2001-12)
We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results ...
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 ...
Variably skewed Brownian motion
(Institute of Mathematical Statistics, 2000-03-01)
Given a standard Brownian motion B, we show that the equation X [subscript] t = x [subscript] 0 + B [subscript] t + [beta](L [to the power of X] [subscript] t ); t [is greater than or equal to] 0 ; has a unique strong solution X. Here L [to the power of X] is the symmetric local time of X at 0, and [beta] is a given differentiable ...
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.
Fiber Brownian motion and the "hot spots" problem
(Duke University Press, 2000-10)
We show that in some planar domains both extrema of the second Neumann eigenfunction lie strictly inside the domain. The main technical innovation is the use of "fiber Brownian motion," a process which switches between two-dimensional and one-dimensional evolution.