Student Probability Seminar
I formerly organized the student probability seminar. 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"
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"
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)
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
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Limiting behavior of Brunet-Derrida particle systems
Introduction to Stein's method; sums of random variables with sparse dependency graphs
Introduction to exchangeable pairs
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
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Concentration inequalities via Stein's method
Chapter 1 and Section 2.1
Sections 2.2 - 2.4
Sections 3.1 - 3.3
Sections 4.1 and 4.2
Concentration results via Brownian motion
Rate functions, Sanov's Theorem
LDPs for Markov chains and random walks
Gibbs conditioning principle
LDPs on general topological spaces
Introduction to nonlinear large deviations