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Now showing items 1-5 of 5

#### 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 ...

#### A Fleming-Viat particle representation of Dirichlet Laplacian

(Springer-Verlag GmbH, 2000-11)

We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. For large N, the particle distribution density converges to the normalized heat equation solution in D ...

#### Efficient Markovian couplings: Examples and counterexamples

(Institute of Mathematical Statistics, 2000-05)

In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the
maximum possible exponential rate, as given by the spectral gap. This notion is of interest not only for its own sake, but also of growing importance
arising from the recent advent ...

#### 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.

#### 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 ...