@@ -147,16 +147,23 @@ Famous distributions in random matrix theory
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# Stochastic processes
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- Provides finite-dimensional matrix representations of stochastic operators.
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-
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- In the following, ` dt ` is the time interval being discretized over and ` t_end ` is the final time.
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-
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- - ` BrownianProcess(dt, t_end) ` generates a vector corresponding to a Brownian random walk starting
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- from time ` t=0 ` and position ` x=0 `
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- - ` WhiteNoiseProcess(dt, t_end) ` generates a vector corresponding to white noise.
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- - ` StochasticAiryProcess(dt, t_end, beta) ` generates the largest eigenvalue corresponding to the
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- stochastic Airy process with real positive ` beta ` . This is known to be distributed in the ` t_end -> Inf `
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- limit to the ` beta ` -Tracy-Widom law.
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+ Julia iterators for stochastic operators.
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+
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+ All subtypes of ` StochasticProcess ` contain at least one field, ` dt ` ,
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+ representing the time interval being discretized over.
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+ The available ` StochasticProcess ` es are
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+
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+ - ` BrownianProcess(dt) ` : Brownian random walk.
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+ The state of the iterator is the cumulative displacement of the random walk.
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+ - ` WhiteNoiseProcess(dt) ` : White noise.
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+ The value of this iterator is ` randn()*dt ` .
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+ The state associated with this iterator is ` nothing ` .
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+ - ` StochasticAiryProcess(dt, beta) ` : stochastic Airy process with real positive ` beta ` .
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+ The value of this iterator in the limit of an infinite number of iterations
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+ is known to follow the ` beta ` -Tracy-Widom law.
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+ The state associated with this iteratior is a ` SymTridiagonal ` matrix whose
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+ largest eigenvalue is the value of this process.
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# Invariant ensembles
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