Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical solution of Dyson Brownian motion and a sampling scheme for
  invariant matrix ensembles   The Dyson Brownian Motion (DBM) describes the stochastic evolution of $N$
points on the line driven by an applied potential, a Coulombic repulsion and
identical, independent Brownian forcing at each point. We use an explicit tamed
Euler scheme to numerically solve the Dyson Brownian motion and sample the
equilibrium measure for non-quadratic potentials. The Coulomb repulsion is too
singular for the SDE to satisfy the hypotheses of rigorous convergence proofs
for tamed Euler schemes. Nevertheless, in practice the scheme is observed to be
stable for time steps of O(1/N^2) and to relax exponentially fast to the
equilibrium measure with a rate constant of O(1) independent of $N$. Further,
this convergence rate appears to improve with $N$ in accordance with O(1/N)
relaxation of local statistics of the Dyson Brownian motion. This allows us to
use the Dyson Brownian motion to sample $N\times N$ Hermitian matrices from the
invariant ensembles. The computational cost of generating $M$ independent
samples is O(MN^4) with a naive scheme, and O(MN^3\log N) when a fast multipole
method is used to evaluate the Coulomb interaction.

17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc