Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interval fragmentations with choice: equidistribution and the evolution
  of tagged fragments   We consider a Markovian evolution on point processes, the $\Psi$--process, on
the unit interval in which points are added according to a rule that depends
only on the spacings of the existing point configuration. Having chosen a
spacing, a new point is added uniformly within it. Building on previous work of
the authors and of Junge, we show that the empirical distribution of points in
such a process is always equidistributed under mild assumptions on the rule,
generalizing work of Junge.
  A major portion of this article is devoted to the study of a particular
growth--fragmentation process, or cell process, which is a type of
piecewise--deterministic Markov process (PDMP). This process represents a
linearized version of a size--biased sampling from the $\Psi$--process. We show
that this PDMP is ergodic and develop the semigroup theory of it, to show that
it describes a linearized version of the $\Psi$--process. This PDMP has
appeared in other contexts, and in some sense we develop its theory under
minimal assumptions.

30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin