A/Prof Tim Garoni

Research Overview

My main area of interest is discrete models in classical statistical mechanics. The study of such models lies at the intersection of mathematical physics, probability theory, combinatorics and computer science. I am interested in both equilibrium models, including the Ising model, self-avoiding walk, percolation, and the Fortuin-Kasteleyn random-cluster model, and also non-equilibrium models such as exclusion processes. A significant portion of my work involves studying the properties of Markov chains which arise in applications of the Monte Carlo method to discrete statistical mechanics. This includes questions such as the speed of mixing of finite Markov chains.

Selected Publications

[1] Deng, Youjin ; Garoni, Timothy M. ; Grimm, Jens ; Nasrawi, Abrahim ; Zhou, Zongzheng. "The length of self-avoiding walks on the complete graph". In: Journal of Statistical Mechanics: Theory and Experiment. 2019 ; Vol. 2019, No. 10. pp. 1-15. https://doi.org/10.1088/1742-5468/ab3da3

[2] Collevecchio, Andrea ; Elçi, Eren Metin ; Garoni, Timothy M. ; Weigel, Martin. "On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model". In: Journal of Statistical Physics. 2018 ; Vol. 170, No. 1. pp. 22-61. https://doi.org/10.1007/s10955-017-1912-x

[3] Zhou, Zongzheng ; Grimm, Jens Christian ; Fang, Sheng ; Deng, Youjin ; Garoni, Tim. "Random-Length Random Walks and Finite-Size Scaling in High Dimensions". In: Physical Review Letters. 2018 ; Vol. 121, No. 18. https://doi.org/10.1103/PhysRevLett.121.185701

[4] Grimm, Jens ; Elçi, Eren Metin ; Zhou, Zongzheng ; Garoni, Timothy M. ; Deng, Youjin. "Geometric Explanation of Anomalous Finite-Size Scaling in High Dimensions". In: Physical Review Letters. 2017 ; Vol. 118, No. 11. https://doi.org/10.1103/PhysRevLett.118.115701

[5] Collevecchio, Andrea ; Garoni, Timothy M. ; Hyndman, Timothy ; Tokarev, Daniel. "The worm process for the Ising model is rapidly mixing". In: Journal of Statistical Physics. 2016 ; Vol. 164, No. 5. pp. 1082-1102. https://doi.org/10.1007/s10955-016-1572-2