All Outputs (2)

An invariance principle for branching diffusions in bounded domains (2018)
Journal Article
Powell, E. (2019). An invariance principle for branching diffusions in bounded domains. Probability Theory and Related Fields, 173(3-4), 999-1062. https://doi.org/10.1007/s00440-018-0847-8

We study branching diffusions in a bounded domain D of Rd in which particles are killed upon hitting the boundary ∂D . It is known that any such process undergoes a phase transition when the branching rate β exceeds a critical value: a multiple of th... Read More about An invariance principle for branching diffusions in bounded domains.

Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation (2018)
Journal Article
Powell, E. (2018). Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation. Electronic Journal of Probability, 23, 1-26. https://doi.org/10.1214/18-ejp157

We show that, for general convolution approximations to a large class of log-correlated fields, including the 2d Gaussian free field, the critical chaos measures with derivative normalisation converge to a limiting measure µ This limiting measure doe... Read More about Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation.