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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 ...
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 ...