Radial symmetric solutions of the Cahn-Hilliard equation with degenerate mobility.
Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy
We consider the following problem: where Φ: Ω ⊂ → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.
Random matrices and permutations, matrix integrals and integrable systems
Random spatial growth with paralyzing obstacles
We study models of spatial growth processes where initially there are sources of growth (indicated by the colour green) and sources of a growth-stopping (paralyzing) substance (indicated by red). The green sources expand and may merge with others (there is no ‘inter-green’ competition). The red substance remains passive as long as it is isolated. However, when a green cluster comes in touch with the red substance, it is immediately invaded by the latter, stops growing and starts to act as a red...
Random walk in a strongly inhomogeneous environment and invasion percolation
Random walks in a Dirichlet environment.
Random walks on finite rank solvable groups
We establish the lower bound , for the large times asymptotic behaviours of the probabilities of return to the origin at even times , for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer , such that any of its finitely generated subgroup admits a generating set of cardinality less or equal to .)
Randomly interacting particle systems : the uniqueness regime
Rationality, property rights and thermodynamic approach to the market equilibrium.
Recurrence of distributional limits of finite planar graphs.
Reduced energy functionals for a three-dimensional fast rotating Bose Einstein condensates
Reflected planar brownian motions, intertwining relations and crossing probabilities
Regularity of the diffusion coefficient matrix for the lattice gas with energy
Relativistic Toda chain with boundary interaction at root of unity.
Remarks on decay of correlations and Witten laplacians III. Application to logarithmic Sobolev inequalities
Renewal convergence rates and correlation decay for homogeneous pinning models.
Renormalization contracts on nested fractals.
Renormalization group approach to zero temperature Bose condensation.
Resonant delocalization for random Schrödinger operators on tree graphs
We analyse the spectral phase diagram of Schrödinger operators on regular tree graphs, with the graph adjacency operator and a random potential given by random variables. The main result is a criterion for the emergence of absolutely continuous spectrum due to fluctuation-enabled resonances between distant sites. Using it we prove that for unbounded random potentials spectrum appears at arbitrarily weak disorder in an energy regime which extends beyond the spectrum of. Incorporating...
Rigorous solution of a mean field spin glass model.