Aidan Petrowski
Open Boundary Stochastic Duality
“The asymmetric simple exclusion process (ASEP) is a Markov chain of particles hopping to the left and right on a one-dimensional lattice with open boundaries connected to particle reservoirs. It is considered as a key stochastic model for a wide variety of transport phenomenon. Although well-understood in a range of cases, an outstanding problem concerns the case of finite lattice size and finite time, which is needed for a proper understanding of the physics in a combined space-time scaling limit.
Recent progress on this matter has been made by using a duality approach for special cases of the ASEP density profile. A key advantage of such dualities is that they can provide insights into complex models through a potentially much simpler dual model.
The primary research concern will be to investigate extensions beyond known results towards dualities for arbitrary density profiles, in order to work toward an understanding of non-equilibrium phase transitions in a combined space-time scaling limit.”
Aidan Petrowski
The University of Melbourne
Aidan Petrowski is a 3rd year student at the University of Melbourne, majoring in pure mathematics alongside a concurrent diploma in Japanese studies. His love for mathematics is wide-reaching, but he has a special interest in the field of mathematical physics for its tendency to combine fascinating problems with beautiful mathematics. Aidan enjoys the collaboration that can be found in academia, and intends to use his Japanese language skills to connect with academics around the world.
Having previously completed research relating to physical combinatorics and separately, compression methods for quantum computer algorithms, Aidan is eager to extend his research experience through the AMSI summer scholarship.
Aidan is a recipient of the Melbourne Chancellor’s scholarship and strives to spread his love of mathematics through his involvement as an executive member of the university’s mathematics society. Outside of his studies, Aidan enjoys exploring nature through hiking, rock climbing and running, as well as reading whenever he can decide on which new book to begin.
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