# @RÉNYI INSTITUTE BUDAPEST

## THE TALKS:

### NATHANAEL BERESTYCKI (Uni Wien): Localisation of a random walk in dimensions $d \ge 3$

Abstract: We study a self-attractive random walk such that each trajectory of length $N$ is penalized by a factor proportional to $\exp(−|R_N |)$, where $R_N$ is the set of sites visited by the walk. We show that the range of such a walk is close to a solid Euclidean ball of radius approximately $\rho_d N^{1/(d+2) }$, for some explicit constant $\rho_d >0$. This proves a conjecture of Bolthausen (1994) who obtained this result in the case d = 2. Joint work with Raphael Cerf (Paris).

### NINA HOLDEN (ETH Zürich): Cardy embedding of random planar maps

Abstract:I will present a joint work with Xin Sun where we prove that uniformly sampled triangulations converge to Liouville quantum gravity under a discrete conformal embedding which we call the Cardy embedding.

### BALÁZS RÁTH (TU Budapest=BME): On the threshold of spread-out contact process percolation

Abstract: In the (spread-out) d-dimensional contact process, vertices can be healthy or infected. With rate one infected sites recover, and with rate lambda they transmit the infection to some other vertex chosen uniformly within a ball of radius R. In configurations sampled from the upper stationary distribution, we study nearest-neighbor site percolation of the set of infected sites and describe the asymptotic behaviour of the associated percolation threshold as R tends to infinity. Joint work with Daniel Valesin.

## DINNER:

After the seminar talks we will go out for dinner (going dutch) to some local restaurant. If you plan to join please do inform the local organizers (Gábor and/or Bálint) about this by Monday, 2nd of March.

## MAPS, DIRECTIONS:

### HOW TO GET TO THE RÉNYI INSTITUTE?

The Rényi Institute is in the very centre of the city. Trains from Vienna arrive at Keleti Station (rather central) with an earlier stop at Kelenföld Station (not so central). The RI is easily accessible from either of these using public transport . Kelenföld is further out, but time-wise it could be faster to get off the train there and take the metro/underground (M4) or the tram (49) as indicated below.

Here is how to come to the RI using public transport:

From Kelenföld Railway Station

From Keleti Railway Station

### HOTELS NEARBY THE RÉNYI INSTITUTE:

Participants who wish to stay overnight in Budapest are kindly asked to make their own arrangements for accommodation.