### 10th World Congress in Probability and Statistics

## Invited Session (live Q&A at Track 3, 10:30PM KST)

## Critical Phenomena in Statistical Mechanics Models (Organizer: Akira Sakai)

### Recent results for critical lattice models in high dimensions

Mark Holmes (University of Melbourne)

### Near-critical avalanches in 2D frozen percolation and forest fires

Pierre Nolin (City University of Hong Kong)

This talk is based on joint works with Rob van den Berg (CWI and VU, Amsterdam) and with Wai-Kit Lam (University of Minnesota).

### Quenched and annealed Ising models on random graphs

Cristian Giardinà (Modena & Reggio Emilia University)

The picture that I will present emerges from several joint works, involving V.H. Can, S. Dommers, C. Giberti, R.van der Hofstad and M.L.Prioriello.

### Q&A for Invited Session 13

###### Session Chair

Akira Sakai (Hokkaido University)

## Privacy (Organizer: Angelika Rohde)

### The Right Complexity Measure in Locally Private Estimation: It is not the Fisher Information

John Duchi (Stanford University)

*local minimax risk*. In contrast to approaches based on worst-case (minimax) error, which are conservative, this allows us to evaluate the difficulty of individual problem instances and delineate the possibilities for adaptation in private estimation and inference. Our main results show that the local modulus of continuity of the estimand with respect to the variation distance—as opposed to the Hellinger distance central to classical statistics—characterizes rates of convergence under locally private estimation for many notions of privacy, including differential privacy and its relaxations. As a consequence of these results, we identify an alternative to the Fisher information for private estimation, giving a more nuanced understanding of the challenges of adaptivity and optimality.

### Sequentially interactive versus non-interactive local differential privacy: estimating the quadratic functional

Lukas Steinberger (University of Vienna)

### Gaussian differential privacy

Weijie Su (University of Pennsylvania)

This is joint work with Jinshuo Dong and Aaron Roth.

### Q&A for Invited Session 15

###### Session Chair

Angelika Rohde (University of Freiburg)

## Random Planar Geometries (Organizer: Nina Holden)

### Markovian infinite triangulations

Thomas Budzinski (École normale supérieure de Lyon)

### Rotational invariance in planar FK-percolation

Ioan Manolescu (Université de Fribourg)

Our result is obtained via a universality theorem for FK-percolation on certain isoradial lattices. This in turn is proved via the star-triangle (or Yang-Baxter) transformation, which may be used to gradually change the square lattice into any of these isoradial lattices, while preserving certain features of the model. It was previously proved that throughout this transformation, the large scale geometry of the model is distorted by at most a limited amount. In the present work we argue that the distortion becomes insignificant as the scale increases. This hinges on the interplay between the inhomogeneity of isoradial models and their embeddings, which compensate each other at large scales.

As a byproduct, we obtain the asymptotic rotational invariance also for models related to FK-percolation, such as the Potts and six-vertex ones. Moreover, the approach described here is fairly generic and may be adapted to other systems which possess a Yang-Baxter transformation. Based on joint work with Hugo Duminil-Copin, Karol Kajetan Kozlowski, Dmitry Krachun and Mendes Oulamara.

### Brownian half-plane excursions, CLE_4 and critical Liouville quantum gravity

Ellen Powell (Durham University)

This is based on a forthcoming joint work with Juhan Aru, Nina Holden and Xin Sun, and describes the analogue of Duplantier-Miller-Sheffield’s “mating-of-trees correspondence” in the critical regime.

### Q&A for Invited Session 24

###### Session Chair

Nina Holden (Swiss Federal Institute of Technology Zürich)