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"

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"

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

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

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

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