Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Single Big Jump Principle in Physical Modelling   The big jump principle is a well established mathematical result for sums of
independent and identically distributed random variables extracted from a fat
tailed distribution. It states that the tail of the distribution of the sum is
the same as the distribution of the largest summand. In practice, it means that
when in a stochastic process the relevant quantity is a sum of variables, the
mechanism leading to rare events is peculiar: instead of being caused by a set
of many small deviations all in the same direction, one jump, the biggest of
the lot, provides the main contribution to the rare large fluctuation. We
reformulate and elevate the big jump principle beyond its current status to
allow it to deal with correlations, finite cutoffs, continuous paths, memory
and quenched disorder. Doing so we are able to predict rare events using the
extended big jump principle in L\'evy walks, in a model of laser cooling, in a
scattering process on a heterogeneous structure and in a class of L\'evy walks
with memory. We argue that the generalized big jump principle can serve as an
excellent guideline for reliable estimates of risk and probabilities of rare
events in many complex processes featuring heavy tailed distributions, ranging
from contamination spreading to active transport in the cell.

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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
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The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph