# Speakers for 2019/20

## Jeff Steif (Chalmers University of Technology, Gothenburg)

### 11th Oct 2019 (Bristol) / 14th Oct 2019 (Bath)

**Fortuin-Kastelyn type representations for Threshold Gaussian and Stable Vectors: aka Divide and Color processes**

We consider the following simple model: one starts with a finite (or countable) set V, a random partition of V and a parameter p in [0,1]. The "Generalized Divide and Color Model" is the {0,1}-valued process indexed by V obtained by independently, for each partition element in the random partition chosen, with probability p assigning all the elements of the partition element the value 1, and with probability 1−p, assigning all the elements of the partition element the value 0. Many models fall into this context:

(1) the 0 external field Ising model (where the random partition is given by FK percolation),

(2) the stationary distributions for the voter model (where the random partition is given by coalescing random walks),

(3) random walk in random scenery and

(4) the original "Divide and Color Model" introduced and studied by Olle Häggström.

In earlier work, together with Johan Tykesson, we studied what one could say about such processes.

In joint work with Malin Palö Forsström, we study the question of which threshold Gaussian and stable vectors have such a representation: (A threshold Gaussian (stable) vector is a vector obtained by taking a Gaussian (stable) vector and a threshold h and looking where the vector exceeds the threshold h). The answer turns out to be quite varied depending on properties of the vector and the threshold; it turns out that h=0 behaves quite differently than h different from 0. Among other results, in the large h regime, we obtain a phase transition in the stability exponent alpha for stable vectors and the critical value is alpha=1/2.

I will also briefly describe some related results by Forsström concerning such questions for the Ising Model with a nonzero external field.

## Beatrice de Tilière (Université Paris Dauphine) - CANCELLED

### Unfortunately cancelled due to the COVID19 epidemic

**Elliptic dimers and genus 1 Harnack curves**

We consider the dimer model on a bipartite periodic graph with elliptic weights introduced by Fock. The spectral curves of such models are in bijection with the set of all genus 1 Harnack curves. We prove an explicit and local expression for the two-parameter family of ergodic Gibbs measures and for the slope of the measures. This is work in progress with Cédric Boutillier and David Cimasoni.

# Past speakers

### 2018/19

**Paolo dai Pra**, University of Padova

Rhythmic behavior in complex stochastic dynamics (Bath)

Thermodynamic limit and phase transitions in non-cooperative games: some mean-ﬁeld examples (Bristol)

### 2017/18

**Thierry Bodineau**, École Polytechnique

Large time asymptotics of a hard sphere gas close to equilibrium (Bath)

Perturbative regimes for deterministic dynamics of a diluted gas of hard spheres (Bristol)

**Fredrik Viklund**, KTH, Stockholm

Loop-erased walk and natural parametrization (Bath)

Convergence of loop-erased walk in the natural parametrization (Bristol)

**Anja Sturm**, University of Goettingen

On classifying genealogies for general (diploid) exchangeable population models (Bath/Bristol)

### Previous speakers

Cristina Toninelli, Jean-Dominique Deuschel, Ryoki Fukushima, Patricia Goncalves, Milton Jara, Herman Thorrison, Laurent Tournier, Jan Swart, Erwin Bolthausen, Tom Mountford, Lorenzo Zambotti, Oriane Blondel, Takashi Kumagai, Krzysztof Burdzy, Ofer Zeitouni, Jason Schweinsberg, Alain-Sol Sznitman, Nina Gantert, Marc Lelarge, Frank Redig.

# General information

Typically one seminar is at the University of Bristol on a Friday, and another at the University of Bath on the following Monday.

View the full list of probability seminars at Bath.

View the full list of probability seminars at Bristol.

The organisers of the seminars are:

Ofer Busani (Bristol)

Tyler Helmuth (Bristol)

Cécile Mailler (Bath)

Marcel Ortgiese (Bath)