Hryniv, Ostap (2012) 'Regular phase in a model of microtubule growth.', Markov processes and related fields., 18 (2). pp. 177-200.
We study a continuous-time stochastic process on strings made of two types of particles, whose dynamics mimics the behaviour of microtubules in a living cell; namely, the strings evolve via a competition between (local) growth/shrinking as well as (global)hydrolysis processes. We show that the velocity of the string end, which determines the long-term behaviour of the system, depends analytically on the growth and shrinking rates. We also identify a region in the parameter space where the velocity is a strictly monotone function of the rates. The argument is based on stochastic domination, large deviations estimates, cluster expansions and semi-martingale techniques.
|Keywords:||Microtubules, Phase transition, Birth-and-death process, Stochastic domination, Coupling, Cluster expansions.|
|Full text:||Full text not available from this repository.|
|Publisher Web site:||http://mech.math.msu.su/~malyshev/abs12.htm|
|Date accepted:||No date available|
|Date deposited:||No date available|
|Date of first online publication:||2012|
|Date first made open access:||No date available|
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