# Probability and Statistics Seminar

## Recent Preprints

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### May 2020:

**Author:** Svante Janson

**Title:** Tree limits and limits of random trees

### April 2020:

**Authors:** Svante Janson, Debleena Thacker

**Title: **Continuous time digital search tree and a border aggregation model

**Authors: **Xing Shi Cai, Guillem Perarneau

**Title: **The giant component of the directed configuration model revisited

### March 2020:

**Authors: **Xing Shi Cai, Guillem Perarneau

**Title:** The diameter of the directed configuration model

**Authors:** Gabriel Berzunza and Cecilia Holmgren

**Title:** The asymptotic distribution of cluster sizes for supercritical percolation on random split trees

**Author: **Svante Janson

**Title: **Central limit theorems for additive functionals and fringe trees in tries.

**Author: **Svante Janson

**Title: **On the independence number of some random trees.

**Authors: **Svante Janson and Wojciech Szpankowski

**Title: **Hidden words statistics for large patterns.

### December 2019

**Authors:** Robert Hancock, Adam Kabela, Dan Král', Taísa Martins, Roberto Parente, Fiona Skerman and Jan Volec

**Title:** No additional tournaments are quasirandom-forcing

## Upcoming seminars in probability and statistics

*Due to the current situation surrounding the corona virus pandemic, the following talks of the probability and statistics seminar have been cancelled*

### 2 April, 2020

Details: **Robin Stephenson****, **University of Sheffield, Ångström 64119, 10:15 - 11:15 am

**Title:** **Multi-type fragmentation trees as scaling limits of Markov branching trees**

**Abstract: **We introduce multi-type Markov Branching trees, which are simple random population tree models where individuals are characterized by their size and their type and give rise to (size,type)-children in a Galton-Watson fashion, with the rule that the size of any individual is a least the sum of the sizes of its children. Assuming that macroscopic size-splittings are rare, we describe the scaling limits of multi-type Markov Branching trees in terms of multi-type fragmentation trees and observe two main different regimes depending on how the rate of type change and the rate of macroscopic splits in a typical path compare. This framework allows us to unify models which may a priori seem quite different, a strength which we illustrate with two notable applications.

The first one concerns the description of the scaling limits of growing models of random trees built by gluing at each step on the current structure a finite tree picked randomly in a finite alphabet of trees, and the second concerns the scaling limits of large multi-type critical Galton-Watson trees when the offspring distributions all have finite second moments. This topic has already been studied but our approach gives a different proof and we improve on previous results by relaxing some hypotheses.

### 16 April, 2020

Details: **Quan Shi****, **Universität Mannheim, Ångström 64119, 10:15 - 11:15 am

### 7 May, 2020

Details: **Gerardo Barrera Vargas, **University of Helsinki, Ångström 64119, 10:15 - 11:15 am

### 14 May, 2020

Details: **Benjamin Dadoun, **University of Bath, Ångström 64119, 10:15 - 11:15 am

### 28 May, 2020

Details: **Alexander Watson, **University College London, Ångström 64119, 10:15 - 11:15 am