Student Probability Seminar

Autumn 2017: We studied non-standard random walk models.  Papers used include:

October 6

October 13

October 20

October 27

November 3

November 10

November 17

November 24

December 1 

December 8

Erik Bates

Andy Tsao

Mark Perlman

Andrea Ottolini

Alex Dunlap

Damian Pavlyshyn

Kevin Yang

Joey Zou

Leila Sloman

Random walks avoiding their past convex hull

Excited random walks

Self-avoiding and loop-erased random walks

Reinforced edge random walk

The parabolic Anderson model

Random walks in cooling random environments

Non-intersecting random walks

< week off >

Non-backtracking random walks

The Bouchaud trap model

Spring 2017: We studied supercritical branching processes and their limiting measures, as well as continuous analogs. Papers used include:

April 14

April 21

April 28

May 5

May 12

May 19

May 26

June 2

Erik Bates

Erik Bates

Alex Zhai

Joey Zou

Cole Graham

Alex Dunlap

Mark Perlman

Andrea Ottolini    

Introduction to supercritical branching processes

The phase transition for branching random walk

Measures on end spaces after renormalization

Some aspects of branching Brownian motion

Fisher-KPP at large times: exploring the logarithmic Bramson shift

It's a bird!  It's a plane!  It's super-Brownian motion!

Time-dependent branching processes

Introduction to de Finetti's theorem(s)

Winter 2017: We studied Interacting Particle Systems from Liggett's book.

January 20

January 27

February 10

February 17

February 24

March 3

March 10

March 17

Alex Dunlap

Alex Dunlap

Andy Tsao

Erik Bates

Alex Dunlap  

Qian Zhao


Beniada Shabani

Introduction to interacting particle systems

Construction and basic ergodicity properties of some interacting particle systems

Monotonicity and positive correlation methods in interacting particle systems

Examples and applications of dual processes

Wave speed of the contact process & an application to the stochastic Fisher-KPP equation

Introduction to the stochastic Ising model

< week off >

Limiting behavior of Brunet-Derrida particle systems

Autumn 2016: We studied Stein's method, referring to the survey by Ross and notes by Chatterjee.      

October 10

October 17

October 24

November 1

November 7

November 14

November 28

December 5

Erik Bates

Paulo Orenstein

Jimmy He

Alex Dunlap

Mark Perlman

Erik Bates

Leila Sloman

Introduction to Stein's method; sums of random variables with sparse dependency graphs

Introduction to exchangeable pairs

Size-bias coupling

Exponential approximation and an application to critical branching processes

Zero-bias coupling and the Lindeberg condition

Geometric approximation with an application to uniform attachment graph model

< week off >

Concentration inequalities via Stein's method

Spring 2016: We followed van Handel's Probability in High Dimension.       

April 8

April 15

April 22

April 29

May 6

May 13

Erik Bates

Erik Bates

Subhabrata Sen

Zhou Fan

Paulo Orenstein

Alex Zhai

Chapter 1 and Section 2.1

Sections 2.2 - 2.4

Sections 3.1 - 3.3

Section 3.4

Sections 4.1 and 4.2

Concentration results via Brownian motion

Winter 2016: We followed Dembo-Zeitouni's Large Deviations Techniques and Applications.

January 21

January 28

February 4

February 11

February 18

February 25

March 3

Erik Bates

Zhou Fan

Alex Dunlap

Subhabrata Sen

Erik Bates

Naomi Feldheim

Alex Zhai

Rate functions, Sanov's Theorem

Cramér's Theorem

Gärtner–Ellis Theorem

LDPs for Markov chains and random walks

Gibbs conditioning principle

LDPs on general topological spaces

Introduction to nonlinear large deviations