A. Giese, R. Bjerkvig, M. E. Berens, and M. Westphal, Cost of Migration: Invasion of Malignant Gliomas and Implications for Treatment, Journal of Clinical Oncology, vol.21, issue.8, p.1624, 2003.
DOI : 10.1200/JCO.2003.05.063

T. Demuth and M. E. Berens, Molecular Mechanisms of Glioma Cell Migration and Invasion, Journal of Neuro-Oncology, vol.6, issue.Pt8, p.217, 2004.
DOI : 10.1007/s11060-004-2751-6

M. Nakada, S. Nakada, T. Demuth, N. L. Tran, D. B. Hoelzinger et al., Molecular targets of glioma invasion, Cellular and Molecular Life Sciences, vol.64, issue.4, p.458, 2007.
DOI : 10.1007/s00018-007-6342-5

H. B. Frieboes, X. Zheng, C. H. Sun, B. Tromberg, R. Gatenby et al., An Integrated Computational/Experimental Model of Tumor Invasion, Cancer Research, vol.66, issue.3, p.1597, 2006.
DOI : 10.1158/0008-5472.CAN-05-3166

A. M. Stein, T. Demuth, D. Mobley, M. Berens, and L. M. Sander, A Mathematical Model of Glioblastoma Tumor Spheroid Invasion in a Three-Dimensional In Vitro Experiment, Biophysical Journal, vol.92, issue.1, p.356, 2007.
DOI : 10.1529/biophysj.106.093468

N. Bellomo, N. K. Li, and P. K. Maini, ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES, Mathematical Models and Methods in Applied Sciences, vol.18, issue.04, p.593, 2008.
DOI : 10.1142/S0218202508002796

J. D. Murray, Mathematical biology II: Spatial models and biomedical applications, 2002.

A. Deutsch and S. Dormann, Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis (Birkhäuser, 2005.

H. Hatzikirou and A. Deutsch, Cellular Automata as Microscopic Models of Cell Migration in Heterogeneous Environments, Curr. Top. Dev. Biol, vol.81, p.401, 2008.
DOI : 10.1016/S0070-2153(07)81014-3

A. R. Anderson, M. A. Chaplain, and K. A. Rejniak, Single-cell-based Models in, Biology and Medicine, 2007.

R. A. Weinberg, The Biology of Cancer (Garland Sciences ? Taylor and Francis, 2007.

P. Tracqui, From passive diffusion to active cellular migration in mathematical models of tumour invasion, Acta Biotheoretica, vol.44, issue.4, p.443, 1995.
DOI : 10.1007/BF00713564

P. Tracqui, G. C. Cruywagen, D. E. Woodward, G. T. Bartoo, J. D. Murray et al., A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth, Cell Proliferation, vol.32, issue.1, p.17, 1995.
DOI : 10.1016/S0022-5193(87)80171-6

D. E. Woodward, J. Cook, P. Tracqui, G. C. Cruywagen, J. D. Murray et al., A mathematical model of glioma growth: the effect of extent of surgical resection, Cell Proliferation, vol.28, issue.6, p.269, 1996.
DOI : 10.1002/1097-0142(197208)30:2<594::AID-CNCR2820300241>3.0.CO;2-2

P. K. Burgess, P. M. Kulesa, J. D. Murray, and J. E. Alvord, The Interaction of Growth Rates and Diffusion Coefficients in a Three-dimensional Mathematical Model of Gliomas, Journal of Neuropathology and Experimental Neurology, vol.56, issue.6, p.704, 1997.
DOI : 10.1097/00005072-199706000-00008

O. Clatz, M. Sermesant, P. Y. Bondiau, S. K. Delinguette, G. Warfield et al., Realistic simulation of the 3-D growth of brain tumors in MR images coupling diffusion with biomechanical deformation, IEEE Transactions on Medical Imaging, vol.24, issue.10, p.1334, 2005.
DOI : 10.1109/TMI.2005.857217

S. Jbabdi, E. Mandonnet, H. Duffau, L. Capelle, K. R. Swanson et al., Simulation of anisotropic growth of low-grade gliomas using diffusion tensor imaging, Magnetic Resonance in Medicine, vol.6, issue.3, p.616, 2005.
DOI : 10.1002/mrm.20625

K. R. Swanson, C. Bridge, J. D. Murray, and J. E. Alvord, Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion, Journal of the Neurological Sciences, vol.216, issue.1, p.1, 2003.
DOI : 10.1016/j.jns.2003.06.001

K. R. Swanson, J. E. Alvord, and J. D. Murray, A quantitative model for differential motility of gliomas in grey and white matter, Cell Proliferation, vol.29, issue.5, p.317, 2000.
DOI : 10.1046/j.1365-2184.2000.00177.x

L. M. Sander and T. S. Deisboeck, Growth patterns of microscopic brain tumors, Physical Review E, vol.66, issue.5, p.51901, 2002.
DOI : 10.1103/PhysRevE.66.051901

M. Castro, C. Molina-parís, and T. S. Deisboeck, Tumor growth instability and the onset of invasion, Physical Review E, vol.72, issue.4, p.41907, 2005.
DOI : 10.1103/PhysRevE.72.041907

N. Bellomo, A. Bellouquid, J. Nieto, and J. Soler, MULTICELLULAR BIOLOGICAL GROWING SYSTEMS: HYPERBOLIC LIMITS TOWARDS MACROSCOPIC DESCRIPTION, Mathematical Models and Methods in Applied Sciences, vol.17, issue.supp01, p.1675, 2007.
DOI : 10.1142/S0218202507002431

H. G. Othmer and T. Hillen, The Diffusion Limit of Transport Equations II: Chemotaxis Equations, SIAM Journal on Applied Mathematics, vol.62, issue.4, p.1222, 2002.
DOI : 10.1137/S0036139900382772

F. Filbet, P. Laurençot, and B. Perthame, Derivation of hyperbolic models for chemosensitive movement, Journal of Mathematical Biology, vol.5, issue.2, p.189, 2005.
DOI : 10.1007/s00285-004-0286-2

Y. Dolak and C. Schmeiser, Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanisms, Journal of Mathematical Biology, vol.23, issue.6, p.595, 2005.
DOI : 10.1007/s00285-005-0334-6

E. A. Codling, M. J. Plank, and S. Benhamou, Random walk models in biology, Journal of The Royal Society Interface, vol.132, issue.3, p.813, 2008.
DOI : 10.1016/j.jtbi.2007.03.026

H. G. Othmer, S. R. Dunbar, and W. Alt, Models of dispersal in biological systems, Journal of Mathematical Biology, vol.25, issue.3, p.263, 1988.
DOI : 10.1007/BF00277392

G. Schaller and M. Meyer-hermann, Continuum versus discrete model: a comparison for multicellular tumour spheroids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.13, issue.6, p.1443, 2006.
DOI : 10.1002/1099-1492(200010)13:6<349::AID-NBM652>3.0.CO;2-X

M. J. Simpson, A. Merrifield, K. A. Landman, and B. D. Hughes, Simulating invasion with cellular automata: Connecting cell-scale and population-scale properties, Physical Review E, vol.76, issue.2, p.21918, 2007.
DOI : 10.1103/PhysRevE.76.021918

A. Q. Cai, K. A. Landman, and B. D. Hughes, Modelling Directional Guidance and Motility Regulation in Cell Migration, Bulletin of Mathematical Biology, vol.400, issue.1, p.25, 2006.
DOI : 10.1007/s11538-005-9028-x

A. R. Anderson and M. A. Chaplain, Continuous and Discrete Mathematical Models of Tumor-induced Angiogenesis, Bulletin of Mathematical Biology, vol.60, issue.5, p.857, 1998.
DOI : 10.1006/bulm.1998.0042

M. Aubert, M. Badoual, S. Féreol, C. Christov, and B. Grammaticos, A cellular automaton model for the migration of glioma cells, Physical Biology, vol.3, issue.2, p.93, 2006.
DOI : 10.1088/1478-3975/3/2/001

C. Kipnis and C. Landim, Scaling Limits of Interacting Particle Systems, 1999.
DOI : 10.1007/978-3-662-03752-2

H. Spohn, Large Scale Dynamics of Interacting Particles, 1991.
DOI : 10.1007/978-3-642-84371-6

S. Turner, J. A. Sherratt, K. J. Painter, and N. J. Savill, From a discrete to a continuous model of biological cell movement, Physical Review E, vol.69, issue.2, p.21910, 2004.
DOI : 10.1103/PhysRevE.69.021910

D. Drasdo, Advances in Complex Systems, p.319, 2005.

M. Alber, N. Chen, T. Glimm, and P. M. Lushnikov, Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description, Physical Review E, vol.73, issue.5, p.51901, 2006.
DOI : 10.1103/PhysRevE.73.051901

M. Aubert, M. Badoual, C. Christov, and B. Grammaticos, A model for glioma cell migration on collagen and astrocytes, Journal of The Royal Society Interface, vol.99, issue.6, p.75, 2008.
DOI : 10.1016/S0959-440X(96)80073-X

U. Frisch, B. Hasslacher, and Y. Pomeau, Lattice-Gas Automata for the Navier-Stokes Equation, Physical Review Letters, vol.56, issue.14, p.1505, 1986.
DOI : 10.1103/PhysRevLett.56.1505

D. Dhumì-eres, P. Lallemand, and U. Frisch, Lattice Gas Models for 3D Hydrodynamics, Europhysics Letters (EPL), vol.2, issue.4, p.291, 1986.
DOI : 10.1209/0295-5075/2/4/006

C. Toninelli and G. Biroli, Jamming Percolation and Glassy Dynamics, Journal of Statistical Physics, vol.93, issue.4, p.731, 2007.
DOI : 10.1007/s10955-006-9177-9

URL : https://hal.archives-ouvertes.fr/hal-00212015

Y. J. Jung, J. P. Garrahan, and D. Chandler, Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids, Physical Review E, vol.69, issue.6, pp.61205-0311396, 2004.
DOI : 10.1103/PhysRevE.69.061205

L. O. Hedges and J. P. Garrahan, Dynamic propensity in a kinetically constrained lattice gas, Journal of Physics: Condensed Matter, vol.19, issue.20, p.205124, 2007.
DOI : 10.1088/0953-8984/19/20/205124

A. C. Pan, J. P. Garrahan, and D. Chandler, Heterogeneity and growing length scales in the dynamics of kinetically constrained lattice gases in two dimensions, Physical Review E, vol.72, issue.4, p.41106, 2005.
DOI : 10.1103/PhysRevE.72.041106

J. Jäckle and A. Krönig, A kinetic lattice-gas model for the triangular lattice with strong dynamic correlations. I. Self-diffusion, Journal of Physics: Condensed Matter, vol.6, issue.38, p.7633, 1994.
DOI : 10.1088/0953-8984/6/38/005

A. Krönig and J. Jäckle, A kinetic lattice-gas model for the triangular lattice with strong dynamic correlations. II. Collective diffusion, Journal of Physics: Condensed Matter, vol.6, issue.38, p.7655, 1994.
DOI : 10.1088/0953-8984/6/38/006

J. Fritz, On the hydrodynamic limit of a one-dimensional Ginzburg-Landau lattice model. Thea priori bounds, Journal of Statistical Physics, vol.46, issue.3-4, p.551, 1987.
DOI : 10.1007/BF01007526

M. Z. Guo, G. C. Papanicolaou, and S. R. Varadhan, Nonlinear diffusion limit for a system with nearest neighbor interactions, Communications in Mathematical Physics, vol.19, issue.1, p.31, 1988.
DOI : 10.1007/BF01218476

S. R. Varadhan, Scaling limits for interacting diffusions, Communications in Mathematical Physics, vol.135, issue.2, p.313, 1991.
DOI : 10.1007/BF02098046

S. R. Varadhan and H. Yau, Diffusive limit of lattice gas with mixing conditions, Asian Journal of Mathematics, vol.1, issue.4, p.623, 1997.
DOI : 10.4310/AJM.1997.v1.n4.a1

C. Deroulers and R. Monasson, Field-theoretic approach to metastability in the contact process, Physical Review E, vol.69, issue.1, p.16126, 2004.
DOI : 10.1103/PhysRevE.69.016126

URL : https://hal.archives-ouvertes.fr/hal-00000638

M. Doi, Second quantization representation for classical many-particle system, Journal of Physics A: Mathematical and General, vol.9, issue.9, p.1465, 1976.
DOI : 10.1088/0305-4470/9/9/008

B. U. Felderhof, Note on spin relaxation of the ising chain, Reports on Mathematical Physics, vol.2, issue.2, p.151, 1971.
DOI : 10.1016/0034-4877(71)90027-9

B. U. Felderhof, Spin relaxation of the Ising chain, Reports on Mathematical Physics, vol.1, issue.3, p.215, 1971.
DOI : 10.1016/S0034-4877(71)80006-X

L. P. Kadanoff and J. Swift, Transport Coefficients near the Critical Point: A Master-Equation Approach, Physical Review, vol.165, issue.1, p.310, 1968.
DOI : 10.1103/PhysRev.165.310

J. L. Vázquez, The Porous Medium Equation, 2007.
DOI : 10.1093/acprof:oso/9780198569039.001.0001

P. L. Garrido, J. L. Lebowitz, C. Maes, and H. Spohn, Long-range correlations for conservative dynamics, Physical Review A, vol.42, issue.4, p.1954, 1990.
DOI : 10.1103/PhysRevA.42.1954

H. Spohn, Long range correlations for stochastic lattice gases in a non-equilibrium steady state, Journal of Physics A: Mathematical and General, vol.16, issue.18, p.4275, 1983.
DOI : 10.1088/0305-4470/16/18/029

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, 1992.

K. R. Swanson, H. L. Harpold, D. L. Peacock, R. Rockne, C. Pennington et al., Velocity of Radial Expansion of Contrast-enhancing Gliomas and the Effectiveness of Radiotherapy in Individual Patients: a Proof of Principle, Clinical Oncology, vol.20, issue.4, p.301, 2008.
DOI : 10.1016/j.clon.2008.01.006

H. M. Young, A. J. Bergner, R. B. Anderson, H. Enomoto, J. Milbrandt et al., Dynamics of neural crest-derived cell migration in the embryonic mouse gut, Developmental Biology, vol.270, issue.2, p.455, 2004.
DOI : 10.1016/j.ydbio.2004.03.015

J. D. Murray, Mathematical biology: I. An Introduction, 2002.

A. Okubo, Diffusion and Ecological Problems, 1980.
DOI : 10.1007/978-1-4757-4978-6

T. P. Witelski, Segregation and mixing in degenerate diffusion in population dynamics, Journal of Mathematical Biology, vol.35, issue.6, p.695, 1997.
DOI : 10.1007/s002850050072

D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, The Journal of Physical Chemistry, vol.81, issue.25, p.2340, 1977.
DOI : 10.1021/j100540a008

J. Hansen and I. R. Mcdonald, Theory of simple liquids ?, 1986.