for this workshop
Gibbsian line ensembles
at the
American Institute of Mathematics, Pasadena, California
organized by
Evgeni Dimitrov, Milind Hegde, and Xuan Wu
This workshop, sponsored by AIM and the NSF, 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:
- Scaling limits of line ensembles in diverse settings (e.g., half-/finite-space, different boundary conditions, presence of spikes).
- Alternative characterizations of line ensembles in KPZ and beyond (area-tilted, general beta, and Bessel line ensembles, etc.)
- Connections to algebraic combinatorics (symmetric functions, vertex models, RSK)
- Links to SDE’s, Markov processes, and dynamics on line ensembles.
- Relations to the directed landscape and the KPZ fixed point.
- Quantitative and qualitative properties of line ensemble (resampling invariance, path regularity, tail probabilities, large deviations principles, etc.)
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than March 10, 2026.
Before submitting an application, please read the description of the AIM style of workshop.
For more information email workshops@aimath.org
