Universal Cumulants and Conformal Invariance in Annihilating Random Walks with Pair Deposition
Abstract
We consider annihilating random walks on the finite one-dimensional integer torus with deposition of pairs of particles, conditioned on an atypical number of particle jumps. In the thermodynamic limit the process undergoes a dynamical phase transition in the universality class of the one-dimensional quantum Ising model in a transverse field. All cumulants of the time-integrated particle current and of the time-integrated activity, defined as the total number of particle jumps up to some time t, are obtained in closed form to leading order in system size L at the critical point. The generating functions of the cumulants near the critical point are proved to be given by two universal quantities, viz., by the central charge c = 1/2 of the Virasoro algebra that characterizes the Ising universality class and universal scaling functions that are obtained in explicit form.
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BibTeX
@article{karevski2026universal,
title = {{Universal Cumulants and Conformal Invariance in Annihilating Random Walks with Pair Deposition}},
author = {D. Karevski and G M Schütz and A. Zahra},
journal = {Mathematical Physics, Analysis and Geometry},
year = {2026},
month = aug,
doi = {10.1007/s11040-026-09588-6},
eprint = {2505.16046},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05766668v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Universal Cumulants and Conformal Invariance in Annihilating Random Walks with Pair Deposition
AU - D. Karevski
AU - G M Schütz
AU - A. Zahra
PY - 2026
DA - 2026/08/26
JO - Mathematical Physics, Analysis and Geometry
DO - 10.1007/s11040-026-09588-6
UR - https://hal.science/hal-05766668v1
AB - We consider annihilating random walks on the finite one-dimensional integer torus with deposition of pairs of particles, conditioned on an atypical number of particle jumps. In the thermodynamic limit the process undergoes a dynamical phase transition in the universality class of the one-dimensional quantum Ising model in a transverse field. All cumulants of the time-integrated particle current and of the time-integrated activity, defined as the total number of particle jumps up to some time t, are obtained in closed form to leading order in system size L at the critical point. The generating functions of the cumulants near the critical point are proved to be given by two universal quantities, viz., by the central charge c = 1/2 of the Virasoro algebra that characterizes the Ising universality class and universal scaling functions that are obtained in explicit form.
SN - 1385-0172
SN - 1572-9656
ER -