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.

Preprints

• M. Dickson and Y. Liu,
  Decay of connection probability in high-dimensional continuum percolation.
  Preprint, 29 pages.
  [preprint@arXiv]

• M. Dickson and M. Heydenreich,
  Mean-field behaviour of the random connection model on hyperbolic space.
  Preprint, 37 pages.
  [preprint@arXiv]

• M. Dickson,
  Non-uniqueness phase in hyperbolic marked random connection models using the spherical transform.
  Preprint, 52 pages.
  [preprint@arXiv]

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

Published Articles

• 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)