All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 56

Showing per page

Giant vacant component left by a random walk in a random d-regular graph

Jiří Černý, Augusto Teixeira, David Windisch (2011)

Annales de l'I.H.P. Probabilités et statistiques

We study the trajectory of a simple random walk on a d-regular graph with d ≥ 3 and locally tree-like structure as the number n of vertices grows. Examples of such graphs include random d-regular graphs and large girth expanders. For these graphs, we investigate percolative properties of the set of vertices not visited by the walk until time un, where u > 0 is a fixed positive parameter. We show that this so-called vacant set exhibits a phase transition in u in the following sense: there...

Long-range self-avoiding walk converges to α-stable processes

Markus Heydenreich (2011)

Annales de l'I.H.P. Probabilités et statistiques

We consider a long-range version of self-avoiding walk in dimension d > 2(α ∧ 2), where d denotes dimension and α the power-law decay exponent of the coupling function. Under appropriate scaling we prove convergence to brownian motion for α ≥ 2, and to α-stable Lévy motion for α < 2. This complements results by Slade [J. Phys. A21 (1988) L417–L420], who proves convergence to brownian motion for nearest-neighbor self-avoiding walk in high dimension.

Mean-field evolution of fermionic systems

Marcello Porta (2014/2015)

Séminaire Laurent Schwartz — EDP et applications

We study the dynamics of interacting fermionic systems, in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitable assumptions on the inital data and on the many-body interaction, the quantum evolution of the system is approximated by a time-dependent quasi-free state. In particular we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent...

Moderate deviations for a Curie–Weiss model with dynamical external field

Anselm Reichenbachs (2013)

ESAIM: Probability and Statistics

In the present paper we prove moderate deviations for a Curie–Weiss model with external magnetic field generated by a dynamical system, as introduced by Dombry and Guillotin-Plantard in [C. Dombry and N. Guillotin-Plantard, Markov Process. Related Fields 15 (2009) 1–30]. The results extend those already obtained for the Curie–Weiss model without external field by Eichelsbacher and Löwe in [P. Eichelsbacher and M. Löwe, Markov Process. Related Fields 10 (2004) 345–366]. The Curie–Weiss model with...

Numerical application of knot invariants and universality of random knotting

Tetsuo Deguchi, Kyoichi Tsurusaki (1998)

Banach Center Publications

We study universal properties of random knotting by making an extensive use of isotopy invariants of knots. We define knotting probability ( P K ( N ) ) by the probability of an N-noded random polygon being topologically equivalent to a given knot K. The question is the following: for a given model of random polygon how the knotting probability changes with respect to the number N of polygonal nodes? Through numerical simulation we see that the knotting probability can be expressed by a simple function of...

Odd cutsets and the hard-core model on ℤ d

Ron Peled, Wojciech Samotij (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider the hard-core lattice gas model on ℤ d and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds C d - 1 / 3 ( log d ) 2 , the model exhibits multiple hard-core measures, thus improving the previous bound of C d - 1 / 4 ( log d ) 3 / 4 given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in ℤ d , the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined combinatorial...

Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics

Mireille Bossy, Nicolas Champagnat, Sylvain Maire, Denis Talay (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Motivated by the development of efficient Monte Carlo methods for PDE models in molecular dynamics, we establish a new probabilistic interpretation of a family of divergence form operators with discontinuous coefficients at the interface of two open subsets of ℝ d . This family of operators includes the case of the linearized Poisson-Boltzmann equation used to compute the electrostatic free energy of a molecule. More precisely, we explicitly construct a Markov process whose infinitesimal generator...

Random walks on finite rank solvable groups

Ch. Pittet, Laurent Saloff-Coste (2003)

Journal of the European Mathematical Society

We establish the lower bound p 2 t ( e , e ) ≿ exp ( − t 1 / 3 ) , for the large times asymptotic behaviours of the probabilities p 2 t ( e , e ) of return to the origin at even times 2 t , 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 r , such that any of its finitely generated subgroup admits a generating set of cardinality less or equal to r .)

Currently displaying 21 – 40 of 56