16 citations · 92 across the 19 of their papers we have counts for
19 papers
Random Walk conditioned to stay above a non-flat floor: curvature effects
Sébastien Ott, Yvan Velenik
Let be and such that . For a (large) positive integer , set for any . We consider a rando…
Finite-time trajectorial estimates for inhomogeneous random walks
Sébastien Ott, Yvan Velenik
We consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit…
Fixed-magnetization Ising model with a slowly varying magnetic field
Yacine Aoun, Sébastien Ott, Yvan Velenik
The motivation for this paper is the analysis of the fixed-density Ising lattice gas in the presence of a gravitational field. This is a seen as a particular instance of an Ising m…
A note on the renormalization group approach to the Central Limit Theorem
Sébastien Ott
Two proofs of the Central Limit Theorem using a renormalization group approach are presented. The first proof is conducted under a third moment assumption and shows that a suitable…
Low temperature asymptotic expansion for classical vector models
Alessandro Giuliani, Sébastien Ott
We consider classical vector models in dimension three and higher and investigate the nature of the low-temperature expansions for their multipoint spin correlations. We pro…
On the two-point function of the Potts model in the saturation regime
Yacine Aoun, Sébastien Ott, Yvan Velenik
We consider the Random-Cluster model on with interactions of infinite range of the form with a norm on and a su…
Ornstein-Zernike behavior for Ising models with infinite-range interactions
Yacine Aoun, Sébastien Ott, Yvan Velenik
We prove Ornstein-Zernike behavior for the large-distance asymptotics of the two-point function of the Ising model above the critical temperature under essentially optimal assumpti…
Failure of Ornstein--Zernike asymptotics for the pair correlation function at high temperature and small density
Y. Aoun, D. Ioffe, S. Ott +1
We report on recent results that show that the pair correlation function of systems with exponentially decaying interactions can fail to exhibit Ornstein-Zernike asymptotics at all…
Delocalisation and absolute-value-FKG in the solid-on-solid model
Piet Lammers, Sébastien Ott
The solid-on-solid model is a model of height functions, introduced to study the interface separating the and phase in the Ising model. The planar solid-on-solid model thus…
Critical prewetting in the 2d Ising model
Dmitry Ioffe, Sébastien Ott, Senya Shlosman +1
In this paper we develop a detailed analysis of critical prewetting in the context of the two-dimensional Ising model. Namely, we consider a two-dimensional nearest-neighbor Ising…
Non-analyticity of the correlation length in systems with exponentially decaying interactions
Yacine Aoun, Dmitry Ioffe, Sébastien Ott +1
We consider a variety of lattice spin systems (including Ising, Potts and XY models) on with long-range interactions of the form , where $ψ(x) =…
Existence and properties of connections decay rate for high temperature percolation models
Sébastien Ott
We consider generic finite range percolation models on under a high temperature assumption (exponential decay of connection probabilities and exponential ratio weak…
Weak mixing and analyticity in Random Cluster and low temperature Ising models
Sébastien Ott
In this note we extend the analysis of a previous paper by the author to the Random Cluster model. The main result being that the pressure of the finite range ferromagnetic Ising m…
Invariance principle for a Potts interface along a wall
Dmitry Ioffe, Sébastien Ott, Yvan Velenik +1
We consider nearest-neighbor two-dimensional Potts models, with boundary conditions leading to the presence of an interface along the bottom wall of the box. We show that, after a…
Weak Mixing and Analyticity of the Pressure in the Ising Model
Sébastien Ott
We prove that the pressure (or free energy) of the finite range ferromagnetic Ising model on is analytic as a function of both the inverse temperature and the ma…
Asymptotics of correlations in the Ising model: a brief survey
Sébastien Ott, Yvan Velenik
We present a brief survey of rigorous results on the asymptotic behavior of correlations between two local functions as the distance between their support diverges, concentrating o…
Sharp Asymptotics for the Truncated Two-Point Function of the Ising Model with a Positive Field
Sébastien Ott
We prove that the correction to exponential decay of the truncated two points function in the homogeneous positive field Ising model is . The proof is based on t…
Asymptotics of even-even correlations in the Ising model
Sébastien Ott, Yvan Velenik
We consider finite-range ferromagnetic Ising models on in the regime . We analyze the behavior of the prefactor to the exponential decay of $\mathrm{Cov}(σ_A,…
Potts models with a defect line
Sébastien Ott, Yvan Velenik
We provide a detailed analysis of the correlation length in the direction parallel to a line of modified coupling constants in the ferromagnetic Potts model on at te…