Abstract
We consider two directed polymer models in the Kardar–Parisi–Zhang (KPZ) universality class: the O’Connell–Yor semi-discrete directed polymer with boundary sources and the continuum directed random polymer with (m, n)-spiked boundary perturbations. The free energy of the continuum polymer is the Hopf–Cole solution of the KPZ equation with the corresponding (m, n)-spiked initial condition. This new initial condition is constructed using two semi-discrete polymer models with independent bulk randomness and coupled boundary sources. We prove that the limiting fluctuations of the free energies rescaled by the 1 / 3rd power of time in both polymer models converge to the Borodin–Péché-type deformations of the GUE Tracy–Widom distribution.
| Original language | English |
|---|---|
| Pages (from-to) | 1-19 |
| Number of pages | 19 |
| Journal | Journal of Theoretical Probability |
| Volume | 2019 |
| DOIs | |
| Publication status | Published - 23 May 2019 |
Funding
Open access funding provided by Budapest University of Technology and Economics (BME). We thank Patrik Ferrari and Benedek Valkó for stimulating discussions related to this project. The work of both authors was supported by the NKFI (National Research, Development and Innovation Office) Grant FK123962. The work of B. Vető was supported by the NKFI Grant PD123994, by the Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the ÚNKP–18–4 New National Excellence Program of the Ministry of Human Capacities.
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty