| Description |
Recent analytical developments to describe diffusive processes in discrete space and time have opened up opportunities to study interaction processes that are generally hard to get to within a continuous space-time description. I will describe some of these advances focusing on first-passage dynamics in the presence of multiple reactive or partially reactive targets and with multiple inert heterogeneities (spatial disorder). I will also show a generalization of the formalism to when the movement statistics is correlated, that is for the one-step non-Markov lattice random walk, and its application to a foraging experiment on ants.
References [1] L. Giuggioli, Exact spatio-temporal dynamics of confined lattice random walks in arbitrary dimensions: a century after Smoluchowski and Pólya, Physical Review X 10(2):021045 (2020). [2] S. Sarvaharman and L. Giuggioli, Closed-form solutions to the dynamics of confined biased lattice random walks in arbitrary dimensions, Physical Review E 102(6):062124 (2020). [3] L. Giuggioli and S. Sarvaharman, Spatio-temporal dynamics of random transmission events: from information sharing to epidemic spread, Journal of Physics A: Mathematical and Theoretical 55(37):375005 (2022). [4] T. Kay and L. Giuggioli, Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statistics, Physical Review Research 4(3):L032039 (2022). [5] D. Das and L. Giuggioli, Discrete space-time resetting model: application to first-passage and transmission statistics, Journal of Physics A: Mathematical and Theoretical 55 (42):424004 (2022). [6] D. Das and L. Giuggioli, Dynamics of lattice random walk within regions composed of different media and interfaces, Journal of Statistical Mechanics: Theory and Experiment 1:013201 (2023). [7] D. Marris, S. Sarvaharman and L. Giuggioli, Exact spatio-temporal dynamics of lattice random walks in hexagonal and honeycomb domains, Physical Review E 107(5):054139 (2023). [8] S. Sarvaharman and L. Giuggioli, Particle-environment interactions in arbitrary dimensions: a unifying analytic framework to model diffusion with inert spatial heterogeneities, Physical Review Research 5(4):043281 (2023). [9] D. Marris, L. Giuggioli, Persistent and anti-persistent motion in bounded and unbounded space: resolution of the first-passage problem. New Journal of Physics 26:073020 (2024). [10] L. Giuggioli, S. Sarvaharman, D. Das, D. Marris and T. Kay, Multi-target search in bounded and heterogeneous environments: a lattice random walk perspective, preprint to appear in 'Target Search Problems' book (2024), arXiv preprint arXiv:2311.00464 |
QLS Seminar - The importance of being ‘discrete’: advances on lattice random walk theories in arbitrary dimensions and lattices
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