## Student Probability Seminar

I formerly organized the student probability seminar. The current organizer is Andrea Ottolini. To join the mailing list "probability-student-run" for the seminar, follow this link, submit your email address, and then confirm your subscription as instructed in the automated email.

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

- Angel, Benjamini, Virág 2003: "Random walks that avoid their past convex hull"
- Zerner 2005: "On the speed of a planar random walk avoiding its past convex hull"
- Benjamini, Wilson 2003: "Excited random walk"
- Lawler 2013: "Intersections of random walks"
- Diaconis 1988: "Recent progress on de Finetti's notions of exchangeability"
- Pemantle 1988: "Phase transition in reinforced random walk and RWRE on trees"
- Pemantle 2007: "A survey of random processes with reinforcement"
- Sabot, Zeng 2016: "A random Schrödinger operator associated with the Vertex Reinforced Jump Process on infinite graphs"
- Hairer, Labbé 2015: "A simple construction of the parabolic Anderson model on R^2"
- König 2016: "The parabolic Anderson model: Random walk in random potential"
- Sinai 1982: "The limiting behavior of a one-dimensional random walk in a random medium"
- Avena, den Hollander 2016: "Random walks in cooling random environments"
- Eischelbacher, König 2008: "Ordered random walks"
- Dyson 1962: "A Brownian-Motion Model for the Eigenvalues of a Random Matrix"
- Alon, Benjamini, Lubetzky, Sodin 2007: "Non-backtracking random walks mix faster"
- Ben Arous, Cerny 2006: "Dynamics of trap models"

October 6

October 13

October 20

October 27

November 3

November 10

November 17

November 24

December 1

December 8

Erik Bates

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:

- Liu 2000: "On generalized multiplicative cascades"
- Franchi 1995: "Chaos multiplicatif: un traitement simple et complet de la fonction de partition"
- Hu, Shi 2009: "Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees"
- Barral, Rhodes, Vargas 2012: "Limiting laws of supercritical branching random walks"
- Berestycki notes: "Topics on branching Brownian motion"
- Lalley, Sellke 1987: "A conditional limit theorem for frontier of a branching Brownian motion"
- Hamel, Nolen, Roquejoffre, Ryzhik 2013: "A short proof of the logarithmic Bramson correction in Fisher-KPP equations"
- Nolen, Roquejoffre, Ryzhik 2016: "Refined long time asymptotics for Fisher-KPP fronts"
- Perkins notes: "Super-Brownian motion and critical stochastic spatial systems"
- Slade 2002: "Scaling limits and super-Brownian motion"
- Lalley, Perkins, Zheng 2014: "A phase transition for measure-valued SIR epidemic processes"
- Bhattacharya, Perlman 2017: "Time-inhomogeneous branching processes conditioned on non-extinction"
- Diaconis 1977: "Finite forms of de Finetti's theorem on exchangeability"
- Diaconis, Freedman 1980: "Finite exchangeable sequences"
- Diaconis, Freedman 1987: "A dozen of de Finetti-style results in search of a theory"

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*