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:
October 6Erik BatesRandom walks avoiding their past convex hull
  
October 13Andy TsaoExcited random walks
   
October 20Mark PerlmanSelf-avoiding and loop-erased random walks

October 27Andrea OttoliniReinforced edge random walk

November 3

November 10

November 17

November 24

December 1 

December 8



Alex Dunlap

Damian Pavlyshyn

Kevin Yang



Joey Zou

Leila Sloman

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
Erik BatesIntroduction to supercritical branching processes
  
April 21

Erik BatesThe phase transition for branching random walk
April 28Alex ZhaiMeasures on end spaces after renormalization

May 5Joey ZouSome aspects of branching Brownian motion

May 12

May 19

May 26

June 2


Cole Graham

Alex Dunlap

Mark Perlman

Andrea Ottolini    


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 20Alex DunlapIntroduction to interacting particle systems
  
January 27Alex DunlapConstruction and basic ergodicity properties of some interacting particle systems
   
February 3Jimmy HeCoupling methods in interacting particle systems

February 10Andy TsaoMonotonicity and positive correlation methods in interacting particle systems

February 17

February 24


March 3

March 10

March 17

Erik Bates

Alex Dunlap  


Qian Zhao

    

Beniada Shabani

Examples and applications of dual processes

Wave speed of the contact process and 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 10Erik BatesIntroduction to Stein's method; sums of random variables with sparse dependency graphs
  
October 17Paulo OrensteinIntroduction to exchangeable pairs
   
October 24Jimmy HeSize-bias coupling

November 1Alex DunlapExponential approximation and an application to critical branching processes

November 7

November 14


November 28

December 5



Mark Perlman

Erik Bates




Leila Sloman

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 8Erik BatesChapter 1 and Section 2.1
   
April 15Erik BatesSections 2.2 - 2.4
   
April 22Subhabrata SenSections 3.1 - 3.3

April 29                  Zhou Fan                                 Section 3.4

May 6

May 13



Paulo Orenstein

Alex Zhai


Sections 4.1 and 4.2

Concentration results via Brownian motion

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

January 21Erik BatesRate functions, Sanov's Theorem
   
January 28Zhou FanCramér's Theorem
   
February 4Alex DunlapGärtner–Ellis Theorem

February 11

February 18

February 25

March 3

Subhabrata Sen

Erik Bates

Naomi Feldheim

Alex Zhai


LDPs for Markov chains and random walks

Gibbs conditioning principle

LDPs on general topological spaces

Introduction to nonlinear large deviations



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