A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit
Grunewald, Natalie ; Otto, Felix ; Villani, Cédric ; Westdickenberg, Maria G.
Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, p. 302-351 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We consider the coarse-graining of a lattice system with continuous spin variable. In the first part, two abstract results are established: sufficient conditions for a logarithmic Sobolev inequality with constants independent of the dimension (Theorem 3) and sufficient conditions for convergence to the hydrodynamic limit (Theorem 8). In the second part, we use the abstract results to treat a specific example, namely the Kawasaki dynamics with Ginzburg–Landau-type potential.
Publié le : 2009-05-15
Classification:  Logarithmic Sobolev inequality,  Hydrodynamic limit,  Spin system,  Kawasaki dynamics,  Canonical ensemble,  Coarse-graining,  60K35,  60J25 
@article{1241024672,
     author = {Grunewald, Natalie and Otto, Felix and Villani, C\'edric and Westdickenberg, Maria G.},
     title = {A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit},
     journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
     volume = {45},
     number = {1},
     year = {2009},
     pages = { 302-351},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1241024672}
}

Grunewald, Natalie; Otto, Felix; Villani, Cédric; Westdickenberg, Maria G. A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp.  302-351. http://gdmltest.u-ga.fr/item/1241024672/