Christian Gorski's Homepage

Research Interests

I am broadly interested in the intersection of probability with geometry topology, and especially its interactions with other areas such as (geometric) group theory, coarse geometry, ergodic theory, and combinatorics. I have done research projects in random processes (percolation, first-passage percolation, random walks) on exotic graph geometries, topological data analysis and manifold learning, and permutons.

Some of my most recent work concerns a natural composition operation on permutons. I have some ideas (with varying levels of concreteness) for projects connecting this to ergodic theory and group theory, and would be very happy to discuss these with potential collaborators.

Preprints

Gorski C. On composition of permutons. (2026) arXiv 

Gorski C. Detection of first homology via random geometric graphs in the thermodynamic regime. (2026)  arXiv Submitted.

Dubin, K., Gorski, C., and Michelen, M. The geometry of the giant component of random geometric graphs. (2026) arXiv Submitted.

Dubin, K., Gorski, C. Lipschitz continuity of the time constant for continuum percolation. arXiv Submitted. (2026)

Chaudkhari, M., Gorski, C., and Silva, E. CLT for lamplighter groups with acylindrically hyperbolic base. (2025) arXiv Submitted.

Gorski, C. and Procaccia, E. B. Chemical distance in graphs of polynomial growth. (2025) arXiv Submitted.

Publications

Gorski, C. Strict monotonicity for first passage percolation on graphs of polynomial growth and quasi-trees. Annals of Probability 52(4): 1487-1537 (July 2024). arXiv 

Auffinger, A. and Gorski, C. Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups. Probability Theory and Related Fields 186, 285-326 (2023). arXiv 

Thesis

Gorski, C. Large-scale geometry of first passage percolation on graphs of polynomial growth. link 

Recorded talks

I gave a mini-course on some classical results in percolation in the Randomness and Geometry Seminar at the Fields Insititute's Thematic Program on Randomness and Geometry (Winter 2024). The course starts from very basics and goes through the proof of the Burton-Keane theorem (uniqueness of the infinite cluster for amenable graphs) and Duminil-Copin and Tassion's proof of sharpness of the phase transition.

Lecture 1: Definitions, weak existence of phase transition.

Lecture 2: Proof of the Burton-Keane theorem (uniqueness of the infinite cluster for amenable graphs).

Lecture 3: More on (non)uniqueness, and some tools---FKG and BK inequalities and Russo's formula.

Lecture 4: Duminil-Copin and Tassion's proof of sharpness of the phase transition.