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README.md

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@@ -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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In the following, `dt` is the time interval being discretized over and `t_end` is the final time.
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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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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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- `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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