6 papers · 1 filter
Thin-shell theory for rotationally invariant random simplices
Johannes Heiny, Samuel Johnston, Joscha Prochno
For fixed functions , consider the rotationally invariant probability density on of the form \[ μ^n(ds) = \frac{1}{Z_n} G(\|s\|_2)\, e^{…
Projections of the uniform distribution on the cube -- a large deviation perspective
Samuel G. G. Johnston, Zakhar Kabluchko, Joscha Prochno
Let be a random vector uniformly distributed on the unit sphere in . Consider the projection of the uniform distribution on the cube $[-1,1…
Sharp concentration for the largest and smallest fragment in a -regular self-similar fragmentation
Piotr Dyszewski, Nina Gantert, Samuel G. G. Johnston +2
We study the asymptotics of the -regular self-similar fragmentation process. For and an integer , this is the Markov process in which each $I…
A Maxwell principle for generalized Orlicz balls
Samuel G. G. Johnston, Joscha Prochno
In [A dozen de {F}inetti-style results in search of a theory, Ann. Inst. H. Poincaré Probab. Statist. 23(2)(1987), 397--423], Diaconis and Freedman studied low-dimensional projecti…
Berry-Esseen bounds for random projections of -balls
Samuel G. G. Johnston, Joscha Prochno
In this work we study the rate of convergence in the central limit theorem for the Euclidean norm of random orthogonal projections of vectors chosen at random from an -ba…
Scaling limits for non-intersecting polymers and Whittaker measures
Samuel G. G. Johnston, Neil O'Connell
We study the partition functions associated with non-intersecting polymers in a random environment. By considering paths in series and in parallel, the partition functions carry na…