Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-conserving zero-range processes with extensive rates under resetting   We consider a non-conserving zero-range process with hopping rate
proportional to the number of particles at each site. Particles are added to
the system with a site-dependent creation rate, and vanish with a uniform
annihilation rate. On a fully-connected lattice with a large number of sites,
the mean-field geometry leads to a negative binomial law for the number of
particles at each site, with parameters depending on the hopping, creation and
annihilation rates. This model can be mapped to population dynamics (if the
creation rates are reproductive fitnesses in a haploid population, and the
hopping rate is the mutation rate). It can also be mapped to a
Bianconi--Barab\'asi model of a growing network with random rewiring of links
(if creation rates are the rates of acquisition of links by nodes, and the
hopping rate is the rewiring rate). The steady state has recently been worked
out and gives rise to occupation numbers that reproduce Kingman's
house-of-cards model of selection and mutation. In this paper we solve the
master equation using a functional method, which yields integral equations
satisfied by the occupation numbers. The occupation numbers are shown to forget
initial conditions at an exponential rate that decreases linearly with the
fitness level. Moreover, they can be computed exactly in the Laplace domain,
which allows to obtain the steady state of the system under resetting. The
result modifies the house-of-cards result by simply adding a skewed version of
the initial conditions, and by adding the resetting rate to the hopping rate.

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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys