Urban, Szymon (2024) Constrained-degree percolation on d-ary trees. Bachelor's Thesis, Mathematics.
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Abstract
We investigate the constrained-degree percolation model on d-ary trees, T_d = (V_d, E_d). It is defined based on the continuous-time percolation model, where aside from the standard sequence of uniform random variables (U_e)_{e in E_d} on [0,1], a constraint k in N is given. Each edge e in E_d opens at time U_e, unless one of its end-vertices is a neighbour to k already open edges at this time. The main result of this thesis is establishing the upper and lower bounds on the critical time of the constrained-degree percolation model on d-ary trees. Using these bounds we conduct initial research on the monotonicity and asymptotic behaviour of the critical time.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Szabo, R. and Donderwinkel, S.A. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 05 Jul 2024 09:07 |
| Last Modified: | 05 Jul 2024 09:07 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/32909 |
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