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 M. Heydenreich,
  Expansion of the critical intensity for the random connection model.
  Preprint, 43 pages.
  [preprint@arXiv]

• A. Caicedo and M. Dickson,
  Critical exponents for marked random connection models.
  Preprint, 49 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 Q. Vogel,
  Formation of infinite loops for an interacting bosonic loop soup.
  Electronic Journal of Probability 29, 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)

• Small Class Instructor for MATH 100: Differential Calculus with Applications (UBC Winter 1 2023/24)

• Co-lecturer for Gibbsian Point Processes with M. Heydenreich (LMU winter term 2022/2023)