> BUCXIV 20.08.18  24.08.18
Probability challenges
The BUC will centre around a collection of short courses earlier in the week. During the short courses, some tractable problems will be offered to PhD students who will be given on the Tuesday. Students have until Friday to solve in groups and present, thereby becoming better familiar with the material.
Organizers
Andreas Kyprianou (University of Bath, UK)
Juan Carlos Pardo (CIMAT, México)
Courses
Course 
Title 
A

Branching Distributional Equations and their Applications This course will be centered around the theory and applications of distributional equations of the form: where the are i.i.d. copies of , independent of the vector , and \Phi is a deterministic map. Such equations arise in a wide range of settings, ranging from the analysis of computer algorithms (e.g. Quicksort and PageRank) and the study of queueing networks with synchronization, to applications in biology and statistical physics. Although the solutions to these equations are not in general unique, we are often interested in one particular solution, the socalled attracting endogenous solution. These special solutions can be constructed on a mathematical structure known as a weighted branching process, and their asymptotic behavior can be explicitly computed in many important cases. To complement the theory, we will also introduce a Monte Carlo algorithm based on the bootstrap that can be effectively used for most choices of \Phi. In terms of applications, the course will focus on two specific cases, the linear equation (known as the smoothing transform) and the maximum equation (known as the highorder Lindley equation). The former appears in the analysis of Quicksort and Google’s PageRank, while the latter in the analysis of queueing networks with synchronization. The PageRank example in particular will allow us to explore in more detail the connection between branching distributional equations and complex networks. In particular, we will discuss two different types of random graph models that, due to their local treelike structure, allow us to make the connection between the graph and a (weighted) branching process precise. The coupling techniques involved lie at the core of much or random graph theory, and are therefore of independent interest. 
B Andreas Kyprianou (University of Bath)

Selfsimilar Markov processes 
C Elie Aidekon (Paris VI)

CLE fragmentation

Timetable
Monday 

08:3009:30 
Breakfast 
09:3010:30 
A 
10:3011:00 
Coffee 
11:0012:00 
B 
12:0012:30 
Coffee 
12:3013:00 
PhD presentation 
13:0013:30 
PhD presentation 
13:3015:00 
Lunch 
15:0017:00 
Work sessions 
17:0018:00 
C 
18:0020:00 
Welcome on the balcony 
Tuesday 

08:3009:30 
Breakfast 
09:3010:30 
B 
10:3011:00 
Coffee 
11:0012:00 
C 
12:0012:30 
Coffee 
12:3013:30 
Cecile Mailler (University of Bath): 
13:3015:00 
Lunch 
15:0017:00 
Work sessions 
17:0018:00 
A 
Wednesday 

08:3009:30 
Breakfast 
09:3010:30 
C 
10:3011:00 
Coffee 
11:0012:00 
A 
12:0012:30 
Coffee 
12:3013:30 
Alex Watson (Manchester): 
13:3015:00 
Lunch 
15:0017:00 
Work sessions 
17:0018:00 
B 
Thursday 

08:3009:30 
Breakfast 
09:3010:30 
C 
10:3011:00 
Coffee 
11:0012:00 
A 
12:0012:30 
Coffee 
12:3013:30 
Cecile Mailler (University of Bath): 
12:3013:00 

13:0015:00 
Lunch 
15:0017:00 
Work sessions 
17:0018:00 
B 
Friday 

08:3009:30 
Breakfast 
09:3010:30 
A 
10:3011:00 
Coffee 
11:0012:00 
B 
12:0012:30 
Coffee 
12:3013:30 
Soluton presentations 
13:3015:00 
Lunch 
15:0017:00 
Solution presentations 
17:0018:00 
C 
Participants
Bath  CIMAT  UNAM  Other 

Andreas Kyprianou
Sandra Palau Emma Horton Dorottya Fekete Minmin Wang Isaac Gonzalez
Cecile Mailler
Alice Callgero

Juan Carlos Pardo
Victor Rivero
Hélene Leman
Natalia Cardona Tobón
Camilo González
Jose Luis Perez
Antonio Murillo

Arno SiriJegousse
Lizbeth Peñaloza Velasco
Alejandro Hernández Wences
Pablo Jorge Hernández Hernández
Miriam Ramírez García
Osvaldo Angtuncio Hernández

Alex Watson
Elie Aidekon
Mariana OlveraCravioto
Kei Noba
