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Ergodic behaviour of “signed voter models”

G. Maillard, T. S. Mountford (2013)

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

We answer some questions raised by Gantert, Löwe and Steif (Ann. Inst. Henri Poincaré Probab. Stat.41(2005) 767–780) concerning “signed” voter models on locally finite graphs. These are voter model like processes with the difference that the edges are considered to be either positive or negative. If an edge between a site x and a site y is negative (respectively positive) the site y will contribute towards the flip rate of x if and only if the two current spin values are equal (respectively opposed)....

Estimate of the Hausdorff measure of the singular set of a solution for a semi-linear elliptic equation associated with superconductivity

Junichi Aramaki (2010)

Archivum Mathematicum

We study the boundedness of the Hausdorff measure of the singular set of any solution for a semi-linear elliptic equation in general dimensional Euclidean space n . In our previous paper, we have clarified the structures of the nodal set and singular set of a solution for the semi-linear elliptic equation. In particular, we showed that the singular set is ( n - 2 ) -rectifiable. In this paper, we shall show that under some additive smoothness assumptions, the ( n - 2 ) -dimensional Hausdorff measure of singular set...

Euler hydrodynamics for attractive particle systems in random environment

C. Bahadoran, H. Guiol, K. Ravishankar, E. Saada (2014)

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

We prove quenched hydrodynamic limit under hyperbolic time scaling for bounded attractive particle systems on in random ergodic environment. Our result is a strong law of large numbers, that we illustrate with various examples.

Exactness of skew products with expanding fibre maps

Thomas Bogenschütz, Zbigniew Kowalski (1996)

Studia Mathematica

We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.

Excited against the tide: a random walk with competing drifts

Mark Holmes (2012)

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

We study excited random walks in i.i.d. random cookie environments in high dimensions, where the k th cookie at a site determines the transition probabilities (to the left and right) for the k th departure from that site. We show that in high dimensions, when the expected right drift of the first cookie is sufficiently large, the velocity is strictly positive, regardless of the strengths and signs of subsequent cookies. Under additional conditions on the cookie environment, we show that the limiting...

Existence and nonexistence of solutions for a model of gravitational interaction of particles, II

Piotr Biler, Danielle Hilhorst, Tadeusz Nadzieja (1994)

Colloquium Mathematicae

We study the existence and nonexistence in the large of radial solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles. The blow-up of solutions defined in the n-dimensional ball with large initial data is connected with the nonexistence of radial stationary solutions with a large mass.

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