Gibbsian line ensembles

August 10 to August 14, 2026

at the

American Institute of Mathematics, Pasadena, California

organized by

Evgeni Dimitrov, Milind Hegde, Xuan Wu, and Zhengye Zhou

Original Announcement

This workshop will focus on new developments in Gibbsian line ensembles, with particular emphasis on their applications to models in the Kardar-Parisi-Zhang (KPZ) universality class.

Over the past decade, Gibbsian line ensembles have become a central framework and indispensable tool for understanding large stochastic systems. In a range of models from statistical mechanics, line ensemble techniques have been used to: establish tightness and refined convergence results, reveal structural properties and hidden symmetries, strongly characterize existing models through limited input, and construct new universal scaling limits.

The workshop aims to advance these directions and explore new applications, with special interest in half-space and finite-space models under various boundary conditions.

Main topics include:

  1. Scaling limits of line ensembles in diverse settings (e.g., half-/finite-space, different boundary conditions, presence of spikes).
  2. Alternative characterizations of line ensembles in KPZ and beyond (area-tilted, general beta, and Bessel line ensembles, etc.)
  3. Connections to algebraic combinatorics (symmetric functions, vertex models, RSK)
  4. Links to SDE’s, Markov processes, and dynamics on line ensembles.
  5. Relations to the directed landscape and the KPZ fixed point.
  6. Quantitative and qualitative properties of line ensemble (resampling invariance, path regularity, tail probabilities, large deviations principles, etc.)

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.