Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the derivative martingale in a branching random walk   We work under the A\"{\i}d\'{e}kon-Chen conditions which ensure that the
derivative martingale in a supercritical branching random walk on the line
converges almost surely to a nondegenerate nonnegative random variable that we
denote by $Z$. It is shown that $\mathbb{E} Z\mathbf{1}_{\{Z\le x\}}=\log
x+o(\log x)$ as $x\to\infty$. Also, we provide necessary and sufficient
conditions under which $\mathbb{E} Z\mathbf{1}_{\{Z\le x\}}=\log x+{\rm
const}+o(1)$ as $x\to\infty$. This more precise asymptotics is a key tool for
proving distributional limit theorems which quantify the rate of convergence of
the derivative martingale to its limit $Z$. The methodological novelty of the
present paper is a three terms representation of a subharmonic function of at
most linear growth for a killed centered random walk of finite variance. This
yields the aforementioned asymptotics and should also be applicable to other
models.

6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: hep-th
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg