Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Antiduality and M\"obius monotonicity: Generalized Coupon Collector
  Problem   For a given absorbing Markov chain $X^*$ on a finite state space, a chain $X$
is a sharp antidual of $X^*$ if the fastest strong stationary time of $X$ is
equal, in distribution, to the absorption time of $X^*$. In this paper we show
a systematic way of finding such an antidual based on some partial ordering of
the state space. We use a theory of strong stationary duality developed
recently for M\"obius monotone Markov chains. We give several sharp antidual
chains for Markov chain corresponding to a generalized coupon collector
problem. As a consequence - utilizing known results on a limiting distribution
of the absorption time - we indicate a separation cutoff (with its window size)
in several chains. We also present a chain which (under some conditions) has a
prescribed stationary distribution and its fastest strong stationary time is
distributed as a prescribed mixture of sums of geometric random variables.

9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc