Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concentration of measure for systems of Brownian particles interacting
  through their ranks   We consider a finite or countable collection of one-dimensional Brownian
particles whose dynamics at any point in time is determined by their rank in
the entire particle system. Using Transportation Cost Inequalities for
stochastic processes we provide uniform fluctuation bounds for the ordered
particles, their local time of collisions, and various associated statistics
over intervals of time. For example, such processes, when exponentiated and
rescaled, exhibit power law decay under stationarity; we derive concentration
bounds for the empirical estimates of the index of the power law over large
intervals of time. A key ingredient in our proofs is a novel upper bound on the
Lipschitz constant of the Skorokhod map that transforms a multidimensional
Brownian path to a path which is constrained not to leave the positive orthant.

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The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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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: plasm-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg