Stefan Junk

Currently

Research interests

I mostly work on the study of random interfaces, which arise naturally in experiments or physical models as the boundary between different phases. One example would be the interface between regions of a ferromagnet where spins are aligned. It is expected that many of these models show a universal behavior, which can be described by the so-called KPZ equation.

Concretely, I have done most of my research on the directed polymer model, which is a discretization of the KPZ equation.

Here are some keywords for my research interests:

• The directed polymer model and first/last passage percolation.
• Random networks, specifically the effect of (long-range) degree correlations in real-world networks
• Random operators
• The random conductance model, and the Mott random walk in particular.
• Oriented percolation.
• (Branching) random walks in random environment.
• Stochastic orders, in particular for the above processes.

Previously

Short CV (updated August 2023).

I have written my PhD thesis supervised by Nina Gantert at TU Munich.

Between November 2019 and June 2021, I was a postdoc hosted by David Croydon and Ryoki Fukushima at RIMS, Kyoto University, and at Tsukuba University. I was supported by the JSPS Postdoctoral Fellowship for Research in Japan (Standard Programm).

Papers and preprints

Submitted

• Local limit theorem for directed polymers beyond the L^2-phase. 2023. (arXiv).
• Fluctuations of partition functions of directed polymers in weak disorder beyond the L^2-phase. 2022. (arXiv).

Accepted

• Extremal regime for one-dimensional Mott variable-range hopping, with David Croydon and Ryoki Fukushima. 2022. To appear in Annales Henri Lebesgue. (arXiv).
• Anomalous scaling regime for one-dimensional Mott variable-range hopping, with David Croydon and Ryoki Fukushima. 2020. To appear in Annals of Applied Probability (arXiv, short video summary).

Published

• Moment characterization of the weak disorder phase for directed polymers in a class of unbounded environments, with Ryoki Fukushima. Electronic Communications in Probability, 2023. (journal, arXiv).
• Stability of weak disorder phase for directed polymer with applications to limit theorems. ALEA Latin American Journal of Probability and Mathematical Statistics, 2023. (journal, arXiv).
• Number of paths in oriented percolation as zero temperature limit of directed polymer, with Ryoki Fukushima. Probability Theory and Related Fields, 2022. (arXiv, short video summary).
• New characterization of the weak disorder phase of directed polymers in bounded random environments. Communications in Mathematical Physics, 2022 (Journal, arXiv, accepted version (small correction in display (17))).
• On large deviation rate functions for a continuous-time directed polymer in weak disorder, with Ryoki Fukushima. Electronic Communications of Probability, 2021(Journal, arXiv).
• Comparison of partition functions in a space-time random environment. Journal of Statistical Physics, 2020. (Journal, arXiv).
• Zero temperature limit for the Brownian directed polymer among Poissonian disasters, with Ryoki Fukushima. Annals of Applied Probability, 2019. (Journal, arXiv)
• A branching random walk among disasters, with Nina Gantert. Electronic Journal of Probability, 2017. (Journal, arXiv)
• On the survival probability of a random walk in random environment with killing. ALEA Latin American Journal of Probability and Mathematical Statistics, 2014. (Journal, arXiv)

PhD Thesis

• Random polymers in disastrous environments

Teaching Experience

Contact

sjunk@math.gakushuin.xyz (replace xyz by ac.jp)