Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Bramson delay in the non-local Fisher-KPP equation   We consider the non-local Fisher-KPP equation modeling a population with
individuals competing with each other for resources with a strength related to
their distance, and obtain the asymptotics for the position of the invasion
front starting from a localized population. Depending on the behavior of the
competition kernel at infinity, the location of the front is either $2t -
({3}/2)\log t + O(1)$, as in the local case, or $2t - O(t^\beta)$ for some
explicit $\beta \in (0,1)$. Our main tools here are alocal-in-time Harnack
inequality and an analysis of the linearized problem with a suitable moving
Dirichlet boundary condition. Our analysis also yields, for any
$\beta\in(0,1)$, examples of Fisher-KPP type non-linearities $f\_\beta$ such
that the front for the localFisher-KPP equation with reaction term $f\_\beta$
is at $2t - O(t^\beta)$.

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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: physics