C. Tsallis, Nonextensive statistical mechanics: A brief introduction, Continuum Mechanics and Thermodynamics, vol.16, issue.3, 2009.
DOI : 10.1007/s00161-004-0174-4

E. Lutz, Anomalous diffusion and Tsallis statistics in an optical lattice, Physical Review A, vol.67, issue.5, p.51402, 2003.
DOI : 10.1103/PhysRevA.67.051402

V. Schwämmle, F. Nobre, and C. Tsallis, q-Gaussians in the porous-medium equation: stability and time evolution, The European Physical Journal B, vol.66, issue.4, p.537546, 2008.
DOI : 10.1140/epjb/e2008-00451-y

C. Vignat and A. Plastino, Why is the detection of q-Gaussian behavior such a common occurrence? Physica A, p.601608, 2009.

A. Ohara and T. Wada, -Gaussian densities and behaviors of solutions to related diffusion equations, Journal of Physics A: Mathematical and Theoretical, vol.43, issue.3, p.35002, 2010.
DOI : 10.1088/1751-8113/43/3/035002
URL : https://hal.archives-ouvertes.fr/halsde-00406815

G. I. Barenblatt, On some unsteady motions of a liquid and a gas in a porous medium, Prikladnaja Matematika i Mechanika, vol.16, p.6778, 1952.

R. E. Pattle, Diusion from an instantaneous point source with concentration dependent coecient, Quart. J. Mech. Appl. Math, vol.12, p.407409, 1959.

M. , D. Pino, and J. Dolbeault, Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diusions, Journal de Mathématiques Pures et Appliquées, vol.81, issue.9, p.847875, 2002.

M. , D. Pino, and J. Dolbeault, The optimal euclidean Lp-Sobolev logarithmic inequality, Journal of Functional Analysis, vol.197, issue.1, p.151161, 2003.

D. Cordero-erausquin, B. Nazaret, and C. Villani, A mass-transportation approach to sharp Sobolev and Gagliardo???Nirenberg inequalities, Advances in Mathematics, vol.182, issue.2, p.307332, 2004.
DOI : 10.1016/S0001-8708(03)00080-X
URL : https://hal.archives-ouvertes.fr/hal-00157943

M. Agueh, Sharp Gagliardo???Nirenberg Inequalities via p-Laplacian Type Equations, Nonlinear Dierential Equations and Applications NoDEA, p.457472, 2008.
DOI : 10.1007/s00030-008-7021-4

F. Pennini, A. Plastino, and G. L. Ferri, Semiclassical information from deformed and escort information measures, Physica A: Statistical Mechanics and its Applications, vol.383, issue.2, p.782796, 2007.
DOI : 10.1016/j.physa.2007.05.009

S. Furuichi, On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics, Journal of Mathematical Physics, vol.50, issue.1, p.1330312, 2009.
DOI : 10.1063/1.3063640

S. Furuichi, On generalized Fisher informations and Crem??r-Rao type inequalities, Journal of Physics: Conference Series, vol.201, p.12016, 2010.
DOI : 10.1088/1742-6596/201/1/012016

J. Naudts, Generalised Exponential Families and Associated Entropy Functions, Entropy, vol.10, issue.3, p.131149, 2008.
DOI : 10.3390/entropy-e10030131
URL : http://doi.org/10.3390/entropy-e10030131

J. Naudts, Abstract, Open Physics, vol.7, issue.3, p.405413, 2009.
DOI : 10.2478/s11534-008-0150-x

E. Lutwak, D. Yang, and G. Zhang, Cram??r???Rao and Moment-Entropy Inequalities for Renyi Entropy and Generalized Fisher Information, IEEE Transactions on Information Theory, vol.51, issue.2, p.473478, 2005.
DOI : 10.1109/TIT.2004.840871

E. Lutwak, S. Lv, D. Yang, and G. Zhang, Extensions of Fisher information and Stam's inequality. Information Theory, IEEE Transactions on, vol.58, issue.3, pp.1319-1327, 2012.

J. Bercher, -Gaussian distributions, Journal of Physics A: Mathematical and Theoretical, vol.45, issue.25, p.45255303, 2012.
DOI : 10.1088/1751-8113/45/25/255303
URL : https://hal.archives-ouvertes.fr/hal-00276749

E. W. Barankin, Locally best unbiased estimates. The Annals of, Mathematical Statistics, vol.20, issue.4, p.477501, 1949.
DOI : 10.1214/aoms/1177729943

I. Vajda, ? ? -divergence and generalized Fisher information, Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, p.223234, 1973.

J. Bercher, -Gaussian distributions, Journal of Mathematical Physics, vol.53, issue.6, p.63303, 2012.
DOI : 10.1063/1.4726197
URL : https://hal.archives-ouvertes.fr/hal-00276749

D. W. Stroock, A Concise Introduction to the Theory of Integration, 1998.

R. A. Horn and C. R. Johnson, Matrix Analysis, 1990.

J. F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems, 2000.
DOI : 10.1007/978-1-4612-1394-9

T. J. Morrison, Functional Analysis: An Introduction to Banach Space Theory, 2000.
DOI : 10.1002/9781118032992

E. Lutwak, D. Yang, and G. Zhang, Moment-Entropy Inequalities for a Random Vector, IEEE Transactions on Information Theory, vol.53, issue.4, p.16031607, 2007.
DOI : 10.1109/TIT.2007.892780

A. J. Stam, Some inequalities satised by the quantities of information of Fisher and Shannon, Information and Control, vol.2, issue.2, p.101112, 1959.

G. B. Folland and A. Sitaram, The uncertainty principle: A mathematical survey, The Journal of Fourier Analysis and Applications, vol.1, issue.2, p.207238, 1997.
DOI : 10.1007/BF02649110

J. C. Angulo, Uncertainty relationships in many-body systems, Journal of Physics A: Mathematical and General, vol.26, issue.22, p.6493, 1993.
DOI : 10.1088/0305-4470/26/22/042

J. C. Angulo, -dimensional many-body systems, Physical Review A, vol.50, issue.1, p.311313, 1994.
DOI : 10.1103/PhysRevA.50.311
URL : https://hal.archives-ouvertes.fr/hal-00259232

I. I. Hirschman, A Note on Entropy, American Journal of Mathematics, vol.79, issue.1, p.152, 1957.
DOI : 10.2307/2372390

I. Bialynicki-birula, Formulation of the uncertainty relations in terms of the R??nyi entropies, Physical Review A, vol.74, issue.5, 2006.
DOI : 10.1103/PhysRevA.74.052101

S. Zozor and C. Vignat, On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles, Physica A: Statistical Mechanics and its Applications, vol.375, issue.2, p.499517, 2007.
DOI : 10.1016/j.physa.2006.09.019
URL : https://hal.archives-ouvertes.fr/hal-00096865

S. Zozor, M. Portesi, P. Sanchez-moreno, and J. S. Dehesa, Position-momentum uncertainty relations based on moments of arbitrary order, Physical Review A, vol.83, issue.5, p.52107, 2011.
DOI : 10.1103/PhysRevA.83.052107

W. Beckner, Inequalities in Fourier Analysis, The Annals of Mathematics, vol.102, issue.1, p.638641, 1975.
DOI : 10.2307/1970980