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PhD in Probability and Mathematical Statistical Mechanics (H/F)

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Français - Anglais

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General information

Reference : UMR8050-ARNLEN-001
Workplace : CRETEIL
Date of publication : Friday, May 15, 2020
Scientific Responsible name : Pr. Arnaud Le Ny (LAMA UMR CNRS 8050 -- UPEC)
Type of Contract : PhD Student contract / Thesis offer
Contract Period : 36 months
Start date of the thesis : 1 October 2020
Proportion of work : Full time
Remuneration : 2 135,00 € gross monthly

Description of the thesis topic

Title of the PhD:

"Random b.c. and Metastates for Ising Models on Random Graphs"

The main goals of the PhD project is to study and develop recently investigated long-range Ising models in any dimensions, and to combine them with recent studies of Ising models on random graphs. The long-range Ising models considered are d-dimensional versions of Dyson model, consisting in Ising spins with polynomially decaying pair-potential. When the decay is slow enough, a phase transition is known to happen in 1d, in a similar way to the 2d nearest-neighbours Ising model, except that the energetic cost to create a droplet of an opposite phase depends on the polynomial decay of the potential.
This makes these models very appealing to interpolate between various dimensions, in a continuous manner. Also, for certain high-dimensions, or, alternatively, low dimensions and
strongly long-range interactions, the lace expansion has been used to show mean-field behavior.
To start the thesis, we propose to investigate the effects of random boundary conditions and possibly mesoscopic fluctuations of interfaces in this context. A few effects have been already
detected (non g-measure property and wetting phenomena, random boundary conditions and metastates in 1d, etc.) and we shall propose a few other directions of investigations.
Parallel to this, we expect the PhD student to consider similar questions on random graphs, where recently a substantial body of work has shown various aspects of the near-critical system,
but even the question what 'random boundary conditions' is unclear depending on the random graph considered. These extensions justify various visits of the student to EURANDOM (UMI CNRS 3022, TU/e, Eindhoven, The Netherlands).

Work Context

The PhD will be performed under the CNRS Program "Thèses internationales 2020 -- Doctorants 80 PRIME" designed to select students in view of collaborations with its international unities (ex-UMI). The affiliation of the recruited candidate will be the laboratory LAMA (UMR CNRS 8050 LAMA) at UPEC (Université Paris Est Créteil) under the direction of Pr. Arnaud Le Ny, but part of the project will imply frequent visits to Eurandom (UMI CNRS 3022 -- TU/e Eindhoven, The Netherlands) under the supervision of Pr. Dr. Remco van der Hoftsad.

Constraints and risks

The recruited candidate must hold a Master 2 in Probability, with solid knowledge in Mathematical Statistical Mechanics and / or on random graphs.

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