Rare Events, Escape Rates and Quasistationarity: Some Exact Formulae
نویسندگان
چکیده
We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of contrained systems to the decay rate of metastable states, are given.
منابع مشابه
Statistical Monitoring of Rare Events in Healthcare
There are miscellaneous quality characteristics in healthcare which are interested to be monitored. However, monitoring each characteristic needs a special statistical method. There are some characteristics with very small incidence rates that it’s usually considered not to be necessary to monitoring them, since their incidence rates are so small that p and np charts are not able to monitor t...
متن کاملAsymptotics of rare events in birth–death processes bypassing the exact solutions
We investigate the near-continuum asymptotics of mean first passage times in some one-variable birth–death processes. The particular problem we address is how to extract mean first passage times in the near-continuum limit from their defining finite-difference equations alone. For the simple class of processes we consider here, exact closed-form solutions for the mean first passage time between...
متن کاملEscape Rates Formulae and Metastablilty for Randomly Perturbed Maps
We provide escape rates formulae for piecewise expanding interval maps with ‘random holes’. Then we obtain rigorous approximations of invariant densities of randomly perturbed metabstable interval maps. We show that our escape rates formulae can be used to approximate limits of invariant densities of randomly perturbed metastable systems.
متن کاملNoise-induced escape on time scales preceding quasistationarity: New developments in the Kramers problem.
Noise-induced escape from the metastable part of a potential is considered on time scales preceding the formation of quasiequilibrium within that part of the potential. It is shown that, counterintuitively, the escape flux may then depend exponentially strongly, and in a complicated manner, on time and friction. (c) 2001 American Institute of Physics.
متن کاملAbsolute rate theories of epigenetic stability.
Spontaneous switching events in most characterized genetic switches are rare, resulting in extremely stable epigenetic properties. We show how simple arguments lead to theories of the rate of such events much like the absolute rate theory of chemical reactions corrected by a transmission factor. Both the probability of the rare cellular states that allow epigenetic escape and the transmission f...
متن کامل