Paul Dario (CY Cergy Paris University): Localisation/delocalisation for the long-range Gaussian chain

This talk will be devoted to the discrete long-range Gaussian chain with $1/r^\alpha$ interactions. I will introduce the model, its history and phase diagram. In this direction, a first notable result is the existence of a roughening phase transition for $\alpha = 2$ established by Kjaer-Hilhorst and Fröhlich-Zegarlinski. For $\alpha > 2$, the model is not expected to undergo a phase transition and a few important results have been recently obtained: Garban characterised the fluctuations of the chain at high temperature (and, in fact, fully identified its scaling limit) and Coquille–van Enter–Le Ny–Ruszel showed the (qualitative) delocalisation of the chain at every inverse temperature. After discussing these results in more details, I will present some quantitative estimates in the low temperature regime with range exponent $\alpha > 2$ obtained in a joint work with L. Coquille and A. Le Ny.