My main fields of interest cover various random marked point processes - including spatial random graph models and marked random connection, as well as bosonic loop soup models and random interlacements. These models exhibit phase transitions in their percolation and condensation behaviour. I am particularly interested in exploring behaviour at and around this transition point, using techniques such as the lace expansion.

Preprints

• M. Dickson,
  Estimating the critical threshold for stretched-out hyperbolic random connection models.
  Preprint, 46 pages.
  [preprint@arXiv]

• M. Dickson and M. Heydenreich,
  The triangle condition for the marked random connection model.
  Preprint, 85 pages.
  To appear in Annales Henri Lebesgue.
  [preprint@arXiv]

Published Articles

• M. Dickson and Y. Liu,
  Decay of connection probability in high-dimensional continuum percolation.
  Mathematical Physics, Analysis and Geometry, 29, 21 (2026).
  [article@SpringerLink, preprint@arXiv]

• M. Dickson and M. Heydenreich,
  Mean-field behaviour of the random connection model on hyperbolic space.
  Journal of the London Mathematical Society, 112(5):e70345 (2025).
  [article@Wiley] (open access)

• M. Dickson,
  Non-uniqueness phase in hyperbolic marked random connection models using the spherical transform.
  Advances in Applied Probability, 58(2):697-744 (2025).
  [article@CambridgeCore] (open access)

• M. Dickson and M. Heydenreich,

Expansion of the critical intensity for the random connection model. 

Combinatorics, Probability and Computing 34 (2):158–209 (2025). 

[article@CambridgeCore] (open access)

• A. Caicedo and M. Dickson,
  Critical exponents for marked random connection models.
  Electronic Journal of Probability 29, no. 151, 1–57 (2024).

[article@ProjectEuclid] (open access)

• M. Dickson and Q. Vogel,
  Formation of infinite loops for an interacting bosonic loop soup.
  Electronic Journal of Probability 29, no. 24, 1–39 (2024).
  [article@ProjectEuclid] (open access)

• S. Adams and M. Dickson,
  Large deviations analysis for random combinatorial partitions with counter terms.
  Journal of Physics A: Mathematical and Theoretical 55 (25):52pp (2022).
  [article@IOPscience] (open access)

• S. Adams and M. Dickson,
  An explicit large deviation analysis of the spatial cycle Huang-Yang-Luttinger model.
  Ann. Henri Poincaré 22, 1535–1560 (2021).
  [article@SpringerLink] (open access)