D. Schickentanz

collaborators

Showing math.PRShow all

3 papers · 1 filter

math.PR2025

Inversions in Random Permutations Under the Ewens Sampling Distribution With and Without a Prescribed Number of Fixed Points

Ross G. Pinsky, Dominic T. Schickentanz

In the first part of the paper, we study the inversion statistic of random permutations under the family $(P_{θ}^{(n)})_{θ \geq 0}$ of Ewens sampling distributions on $S_{n}$ . W…

math.PR2023

Brownian motion conditioned to have restricted $L_{2}$ -norm

Frank Aurzada, Mikhail Lifshits, Dominic T. Schickentanz

We condition a Brownian motion on having an atypically small $L_{2}$ -norm on a long time interval. The obtained limiting process is a non-stationary Ornstein-Uhlenbeck process.

math.PR2023

Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion

Frank Aurzada, Martin Kolb, Dominic T. Schickentanz

We show that a Brownian motion on $R_{\geq 0}$ which is allowed to spend a total of $s > 0$ time units outside a bounded interval does not leave the interval at all. This c…

Inversions in Random Permutations Under the Ewens Sampling Distribution With and Without a Prescribed Number of Fixed Points

Brownian motion conditioned to have restricted L2​-norm

Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion

Brownian motion conditioned to have restricted $L_{2}$ -norm