Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: PhD thesis "Extreme value statistics of strongly correlated systems:
  fermions, random matrices and random walks"   In this thesis, we study three physically relevant models of strongly
correlated random variables: trapped fermions, random matrices and random
walks. In the first part, we show several exact mappings between the ground
state of a trapped Fermi gas and ensembles of random matrix theory. The Fermi
gas is inhomogeneous in the trapping potential and in particular there is a
finite edge beyond which its density vanishes. Going beyond standard
semi-classical techniques (such as local density approximation), we develop a
precise description of the spatial statistics close to the edge. This
description holds for a large universality class of hard edge potentials. We
apply these results to compute the statistics of the position of the fermion
the farthest away from the centre of the trap, the number of fermions in a
given domain (full counting statistics) and the related bipartite entanglement
entropy. Our analysis also provides solutions to open problems of extreme value
statistics in random matrix theory. We obtain for instance a complete
description of the fluctuations of the largest eigenvalue in the complex
Ginibre ensemble. In the second part of the thesis, we study extreme value
questions for random walks. We consider the gap statistics, which requires to
take explicitly into account the discreteness of the process. This question
cannot be solved using the convergence of the process to its continuous
counterpart, the Brownian motion. We obtain explicit analytical results for the
gap statistics of the walk with a Laplace distribution of jumps and provide
numerical evidence suggesting the universality of these results.

24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio