18 citations · 35 across the 11 of their papers we have counts for
12 papers
Local Central Limit Theorem for unbounded long-range potentials
Eric O. Endo, Roberto Fernández, Vlad Margarint +1
We prove the equivalence between the integral central limit theorem and the local central limit theorem for two-body potentials with long-range interactions on the lattice $\mathbb…
On Long Range Ising Models with Random Boundary Conditions
Eric O. Endo, Aernout C. D. van Enter, Arnaud Le Ny
We consider polynomial long-range Ising models in one dimension, with ferromagnetic pair interactions decaying with power (for ), and prepared with randomly chos…
Local Central Limit Theorem for Long-Range Two-Body Potentials at Sufficiently High Temperatures
Eric O. Endo, Vlad Margarint
Dobrushin and Tirozzi [14] showed that, for a Gibbs measure with the finite-range potential, the Local Central Limit Theorem is implied by the Integral Central Limit Theorem. Campa…
Long-Range Ising Models: Contours, Phase Transitions and Decaying Fields
Lucas Affonso, Rodrigo Bissacot, Eric O. Endo +1
Inspired by Fröhlich-Spencer and subsequent authors who introduced the notion of contour for long-range systems, we provide a definition of contour and a direct proof for the phase…
Infinite DLR Measures and Volume-Type Phase Transitions on Countable Markov Shifts
Elmer R. Beltrán, Rodrigo Bissacot, Eric O. Endo
We consider the natural definition of DLR measure in the setting of -finite measures on countable Markov shifts. We prove that the set of DLR measures contains the set of confor…
The roles of random boundary conditions in spin systems
Eric O. Endo, Aernout C. D. van Enter, Arnaud Le Ny
Random boundary conditions are one of the simplest realizations of quenched disorder. They have been used as an illustration of various conceptual issues in the theory of disordere…
Local limits of spatial Gibbs random graphs
Eric Ossami Endo, Daniel Valesin
We study the spatial Gibbs random graphs introduced in [MV16] from the point of view of local convergence. These are random graphs embedded in an ambient space consisting of a line…
Contour methods for long-range Ising models: weakening nearest-neighbor interactions and adding decaying fields
Rodrigo Bissacot, Eric O. Endo, Aernout C. D. van Enter +2
We consider ferromagnetic long-range Ising models which display phase transitions. They are long-range one-dimensional Ising ferromagnets, in which the interaction is given by $J_{…
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…
Dyson models under renormalization and in weak fields
R. Bissacot, E. O. Endo, A. C. D. van Enter +3
We consider one-dimensional long-range spin models (usually called Dyson models), consisting of Ising ferromagnets with slowly decaying long-range pair potentials of the form $\fra…
Stability of the Phase Transition of Critical-Field Ising Model on Cayley trees under Inhomogeneous External Fields
Rodrigo Bissacot, Eric Ossami Endo, Aernout C. D. van Enter
We consider the ferromagnetic Ising model with spatially dependent external fields on a Cayley tree, and we investigate the conditions for the existence of the phase transition for…
Counting Contours on Trees
Noga Alon, Rodrigo Bissacot, Eric Ossami Endo
We calculate the exact number of contours of size containing a fixed vertex in -ary trees and provide sharp estimates for this number for more general trees. We also obtain…