Interacting Particle Systems learning seminar

This is a reading group for students interested in recent developments in interacting particle processes.

Meeting time: Fridays at 12:30pm

Location: 2-131

Contact: Yi Sun (yisun [at]

Spring 2013 Schedule

Meeting Date and Time Room
0 Thursday, February 7 4pm 2-146 -- Organizational Meeting --
1 Friday, February 15 1pm 2-131 Yi Sun Macdonald measures and processes [BC11] Chapter 2
2 Friday, February 22 1pm 2-131 Jeffrey Kuan Dynamics on Macdonald processes [BC11] Chapter 2
3 Friday, March 1 1pm 2-131 Jeffrey Kuan Macdonald processes and q-TASEP [BC11] Chapter 3
4 Friday, March 8 12:30pm 2-131 Xin Sun Gaussian Free Field [She03], [Ken00], [BF08]
-- Friday, March 15 3pm 2-146 -- Alexey Bufetov's talk on "2d GFF via noncommutative moments" --
5 Friday, March 22 12:30pm 2-131 Yi Sun Whittaker processes [BC11] Chapter 4
-- Friday, March 29 3pm 2-146 -- Ivan Corwin's talk on "Discrete time q-TASEPs and their integrability" --
-- Friday, April 5 3pm 2-146 -- Ivan Corwin's talk on "Rigorous applications of the replica method" --
6 Wednesday, April 24 6:00pm 2-131 Konstantin Matveev Geometric RSK [NY04] and Konstantin's Notes
7 Friday, May 3 1:00pm 2-131 Konstantin Matveev O'Connell-Yor Directed Polymer [OCo09]
8 Monday, May 13 10:00am SC 530 Alisa Knizel Random Matrices and Random Permutations [Oko99]

Fall 2012 Schedule

Meeting Date and Time Room
0 Thursday, October 11 4pm 2-103 Organizational Meeting
1 Tuesday, October 23 4pm 2-142 Jeffrey Kuan Overview
2 Tuesday, October 30 4pm 2-142 Yi Sun TASEP with step intial conditions [Joh99]
3 Tuesday, November 6 4pm 2-142 Asad Lodhia TASEP with flat initial conditions [BFPS06]
-- Tuesday, November 13 3pm Harvard SC 232 -- Craig Tracy's talk on "Bethe Ansatz Methods in Stochastic Integrable Models"
4 Tuesday, November 20 4pm 2-142 Yi Sun Bethe ansatz for ASEP [Sch97], [TW07]
5 Tuesday, December 4 4pm 2-142 Jeffrey Kuan Duality [BCS12]


  • Seminar at the Courant Institute, 2008-2009.


  • [Lig07] = T. Liggett, Interacting particle systems - An introduction.
  • [FS10] = P. L. Ferrari and H. Spohn, Random growth models.
  • [Cor11] = I. Corwin, The Kardar-Parisi-Zhang equation and universality class.


  • [Joh99] = K. Johansson, Shape fluctuations and random matrices.
  • [PS01] = M. Praofer and H. Spohn, Current fluctuations for TASEP.
  • [FS05] = P. L. Ferrari and H. Spohn, Scaling limit for the space-time covariance of the stationary TASEP.
  • [BFPS06] = A. Borodin, P. L. Ferrari, M. Prahofer, and T. Sasamoto, Fluctuation properties of the TASEP with periodic initial configuration.
  • [BFS07] = A. Borodin, P. L. Ferrari, and T. Sasamoto, Transition between Airy_1 and Airy_2 processes and TASEP fluctuations.
  • [BC09] = G. Ben Arous and I. Corwin, Current fluctuations for TASEP: A proof of the Prähofer-Spohn conjecture.


  • [Sch97] = G. Schutz, Exact solution of the master equation for ASEP.
  • [BS06] = M. Balazs and T. Seppalainen, Order of current variance and diffusivity in ASEP.
  • [TW07] = C. Tracy and H. Widom, Integral formulas for ASEP.
  • [TW08] = C. Tracy and H. Widom, A Fredholm determinant representation in ASEP.
  • [TW08b] = C. Tracy and H. Widom, Asymptotics in ASEP with step initial condition.
  • [TW11] = C. Tracy and H. Widom, Formulas and Asymptotics for ASEP.
  • [IS10] = T. Imamura and T. Sasamoto, Current moments of 1D ASEP by duality.
  • [BCS12] = A. Borodin, I. Corwin, and T. Sasamoto, From duality to determinants for q-TASEP and ASEP.

    Macdonald processes

  • [BC11] = A. Borodin and I. Corwin, Macdonald processes.

    Gaussian Free Field

  • [Ken00] = R. Kenyon, Dominos and the Gaussian free field.
  • [She03] = S. Sheffield, Gaussian free fields for mathematicians.
  • [BF08] = A. Borodin and P. Ferrari, Anisotropic growth of random surfaces in 2+1 dimensions.

    Geometric RSK

  • [NY04] = M. Noumi and Y. Yamada, Tropical RSK correspondence and birational Weyl group actions.
  • [OCo09] = N. O'Connell, Directed polymers and the quantum Toda lattice.

    Random matrices over finite fields

  • [Fu97] = J. Fulman, The Rogers-Ramanujan identities, the finite general linear groups, and the Hall-Littlewood polynomials.
  • [Fu97b] = J. Fulman, Probabilistic measures and algorithms arising from the Macdonald symmetric functions
  • [Fu97c] = J. Fulman, A probabilistic approach toward the finite general linear and unitary groups.
  • [Fu00] = J. Fulman, Random matrix theory over finite fields: a survey.
  • [Fu01] = J. Fulman, GL(n,q) and increasing subsequences in nonuniform random permutations.
  • [FG12] = J. Fulman and L. Goldstein, Stein's method and the rank distribution of random matrices over finite fields.

    Macdonald polynomials

  • [LO09] = A. Lascoux and S. Ole Warnaar, Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series.


  • [Oko99] = A. Okounkov, Random matrices and random permutations.

    Last updated: 05.07.13