I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Reviews of Modern Physics, vol.91, issue.196, p.885, 2008.
DOI : 10.1103/PhysRevLett.91.250401
URL : https://hal.archives-ouvertes.fr/hal-00195515

S. Giorgini, L. P. Pitaevski, and S. Stringari, Theory of ultracold atomic Fermi gases, Reviews of Modern Physics, vol.77, issue.4, p.1215, 2008.
DOI : 10.1103/PhysRevLett.92.120403
URL : http://arxiv.org/pdf/0706.3360v2.pdf

G. D. Mahan, Many particle physics, 1981.

Y. Castin, Basic theory tools for degenerate Fermi gases, Proceedings of the International School of Physics Enrico Fermi Ultra-cold Fermi Gases, p.612613, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00122049

W. Kohn and A. E. Mattsson, Edge Electron Gas, Physical Review Letters, vol.68, issue.16, p.3487, 1998.
DOI : 10.1119/1.1972842

V. Eisler, Universality in the Full Counting Statistics of Trapped Fermions, Physical Review Letters, vol.16, issue.8, p.80402, 2013.
DOI : 10.1103/PhysRevLett.108.186806

R. Marino, S. N. Majumdar, G. Schehr, and P. Vivo, Phase Transitions and Edge Scaling of Number Variance in Gaussian Random Matrices, Physical Review Letters, vol.112, issue.25, p.254101, 2014.
DOI : 10.1088/1751-8113/46/2/022001
URL : https://hal.archives-ouvertes.fr/hal-01053568

D. S. Dean, P. L. Doussal, S. N. Majumdar, and G. Schehr, Finite-Temperature Free Fermions and the Kardar-Parisi-Zhang Equation at Finite Time, Physical Review Letters, vol.2, issue.11, p.110402, 2015.
DOI : 10.1016/0370-2693(91)90916-E
URL : https://hal.archives-ouvertes.fr/hal-01135370

D. S. Dean, P. L. Doussal, S. N. Majumdar, and G. Schehr, -dimensional trap, EPL (Europhysics Letters), vol.112, issue.6, p.60001, 2015.
DOI : 10.1209/0295-5075/112/60001
URL : https://hal.archives-ouvertes.fr/jpa-00251192

R. Marino, S. N. Majumdar, G. Schehr, and P. Vivo, -ensembles of random matrices: Applications to trapped fermions at zero temperature, Physical Review E, vol.72, issue.3, p.32115, 2016.
DOI : 10.1209/0295-5075/112/60001
URL : https://hal.archives-ouvertes.fr/hal-00017793

Y. V. Fyodorov, Introduction to the random matrix theory: Gaussian Unitary Ensemble and beyond, Math. Soc. Lect. Note Ser, vol.322, p.31, 2005.
DOI : 10.1017/CBO9780511550492.003
URL : http://arxiv.org/abs/math-ph/0412017

C. A. Tracy and H. Widom, Level-spacing distributions and the Airy kernel, Communications in Mathematical Physics, vol.21, issue.1, p.151, 1994.
DOI : 10.1002/j.1538-7305.1961.tb03976.x
URL : http://arxiv.org/abs/hep-th/9210074

J. E. Galambosr, The Asymptotic Theory of Extreme Order Statistics, 1987.

J. Ginibre, Statistical Ensembles of Complex, Quaternion, and Real Matrices, Journal of Mathematical Physics, vol.6, issue.3, p.440, 1965.
DOI : 10.1063/1.1704008

B. A. Khoruzhenko and H. J. Sommers, Non-Hermitian ensembles, in The Oxford Handbook of Random Matrix, 2011.

B. Rider, A limit theorem at the edge of a non-Hermitian random matrix ensemble, Journal of Physics A: Mathematical and General, vol.36, issue.12, p.3401, 2003.
DOI : 10.1088/0305-4470/36/12/331

F. D. Cunden, F. Mezzadri, and P. Vivo, Large Deviations of Radial Statistics in the Two-Dimensional One-Component Plasma, Journal of Statistical Physics, vol.33, issue.164, p.1062, 2016.
DOI : 10.1088/0305-4470/33/10/307

D. Chafa¨?chafa¨? and S. Péché, A Note on the Second Order Universality at the Edge of Coulomb Gases on the Plane, Journal of Statistical Physics, vol.114, issue.164, p.368, 2014.
DOI : 10.1007/978-3-662-03329-6

K. Johansson, Random matrices and determinantal processes, in Lecture Notes of the Les Houches Summer School, pp.math- ph, 2005.

A. Borodin, Determinantal point processes, in The Oxford Handbook of Random Matrix Theory, 2011.

M. Moshinsky and Y. F. Smirnov, The Harmonic oscillator in modern physics, Contempory Concepts in Physics, 1996.

C. Nadal and S. N. Majumdar, Nonintersecting Brownian interfaces and Wishart random matrices, Physical Review E, vol.36, issue.6, p.61117, 2009.
DOI : 10.1103/PhysRevLett.101.216809
URL : https://hal.archives-ouvertes.fr/hal-00400076

I. M. Johnstone, components analysis, The Annals of Statistics, vol.29, issue.2, p.295, 2001.
DOI : 10.1214/aos/1009210544

A. Edelman and M. L. Croix, Random Matrices: Theory Appl, p.1550021, 2015.

D. S. Dean and S. N. Majumdar, Extreme value statistics of eigenvalues of Gaussian random matrices, Physical Review E, vol.36, issue.4, p.41108, 2008.
DOI : 10.1063/1.530529
URL : https://hal.archives-ouvertes.fr/hal-00303729

P. , L. Doussal, S. N. Majumdar, and G. Schehr, We use formula (55) and (57) of the Supp, Mat. of the arXiv version, vol.113, issue.60004, 2016.

A. M. Garcia-garcia, S. M. Nishigaki, and J. J. Verbaarschot, Critical statistics for non-Hermitian matrices, Physical Review E, vol.46, issue.1, p.16132, 2001.
DOI : 10.1007/BF01013377

A. M. Garcia-garcia and J. J. Verbaarschot, Chiral random matrix model for critical statistics, Nuclear Physics B, vol.586, issue.3, p.668, 2000.
DOI : 10.1016/S0550-3213(00)00362-X
URL : http://arxiv.org/abs/hep-th/0003159

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf et al., Single-atom imaging of fermions in a quantum-gas microscope, Nature Physics, vol.56, issue.9, p.738, 2015.
DOI : 10.1103/PhysRevA.56.4815

M. F. Parsons, F. Huber, A. Mazurenko, C. S. Chiu, W. Setiawan et al., in an Optical Lattice, Physical Review Letters, vol.114, issue.21, p.213002, 2015.
DOI : 10.1103/PhysRevLett.107.165301

W. S. Bakr, J. I. Gillen, A. Peng, S. Folling, and M. Greiner, A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice, Nature, vol.79, issue.7269, p.74, 2009.
DOI : 10.1103/PhysRevA.80.021602

J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch et al., Single-atom-resolved fluorescence imaging of an atomic Mott insulator, Nature, vol.78, issue.7311, p.68, 2010.
DOI : 10.1103/PhysRevA.79.061601
URL : https://hal.archives-ouvertes.fr/hal-01397842

W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon et al., Probing the Superfluid-to-Mott Insulator Transition at the Single-Atom Level, Science, vol.74, issue.16, p.547, 2010.
DOI : 10.1103/PhysRevA.74.013622

A. Omran, M. Boll, T. A. Hilker, K. Kleinlein, G. Salomon et al., Microscopic Observation of Pauli Blocking in Degenerate Fermionic Lattice Gases, Physical Review Letters, vol.115, issue.26, p.263001, 2015.
DOI : 10.1038/nature10748

G. J. Edge, R. Anderson, D. Jervis, D. C. Mckay, R. Day et al., Imaging and addressing of individual fermionic atoms in an optical lattice, Physical Review A, vol.92, issue.6, p.63406, 2015.
DOI : 10.1103/PhysRevLett.99.067001