30 citations · 76 across the 10 of their papers we have counts for
11 papers
Extremal inhomogeneous Gibbs states for SOS-models and finite-spin models on trees
Loren Coquille, Christof Kuelske, Arnaud Le Ny
We consider -valued -SOS-models with nearest neighbor interactions of the form , and finite-spin ferromagnetic models on regular trees. This includes the…
Decimations for One- and Two-dimensional Ising and Rotator Models II: Continuous versus Discrete Symmetries
Matteo D'Achille, Arnaud Le Ny, Aernout C. D. van Enter
We show how decimated Gibbs measures which have an unbroken continuous symmetry due to the Mermin-Wagner theorem, although their discrete equivalents have a phase transition, still…
Decimations for Two-dimensional Ising and Rotator Models I
Matteo D'Achille, Aernout C. D. van Enter, Arnaud Le Ny
We extend proofs of non-Gibbsianness of decimated Gibbs measures at low temperatures to include long-range, as well as vector-spin interactions. Our main tools consist in a two-dim…
Almost Gibbsian Measures on a Cayley Tree
Matteo D'Achille, Arnaud Le Ny
We consider the ferromagnetic n.n Ising model on Cayley trees in absence of external fields submitted to a modified majority rule transformation with overlapping cells already know…
Gradient Gibbs measures for the SOS model with countable values on a Cayley tree
F. Henning, C. Kuelske, A. Le Ny +1
We consider an SOS (solid-on-solid) model, with spin values from the set of all integers, on a Cayley tree of order k and are interested in translation-invariant gradient Gibbs mea…
Entropic repulsion and lack of the -measure property for Dyson models
Rodrigo Bissacot, Eric Ossami Endo, Aernout C. D. van Enter +1
We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not -measures. The…
Persistent random walks. II. Functional Scaling Limits
Peggy Cénac, Arnaud Le Ny, Basile De Loynes +1
We give a complete and unified description -- under some stability assumptions -- of the functional scaling limits associated with some persistent random walks for which the recurr…
On the mathematical consequences of binning spike trains
B. Cessac, A. Le Ny, E. Loecherbach
We initiate a mathematical analysis of hidden effects induced by binning spike trains of neurons. Assuming that the original spike train has been generated by a discrete Markov pro…
Decimation of the Dyson-Ising Ferromagnet
Aernout van Enter, Arnaud Le Ny
We study the decimation to a sublattice of half the sites, of the one-dimensional Dyson-Ising ferromagnet with slowly decaying long-range pair interactions of the form $\frac{1}{{|…
Persistent random walks
Peggy Cénac, Basile De Loynes, Arnaud Le Ny +1
We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this pa…
Range of a Transient 2d-Random Walk
Arnaud Le Ny
We study the range of a planar random walk on a randomly oriented lattice, already known to be transient. We prove that the expectation of the range grows linearly, in both the que…