More Like this

1. Quaternionic Brownian Windings

   https://doi.org/10.1007/s10959-020-01034-9  

   Baudoin, Fabrice; Demni, Nizar; Wang, Jing (September 2020, Journal of Theoretical Probability)

   null (Ed.)

   We define and study the three-dimensional windings along Brownian paths in the quaternionic Euclidean, projective and hyperbolic spaces. In particular, the asymp- totic laws of these windings are shown to be Gaussian for the flat and spherical geometries while the hyperbolic winding exhibits a different long time-behavior. The corresponding asymptotic law seems to be new and is related to the Cauchy relativistic distribution. 

   more » « less
2. Brownian axionlike particles

   https://doi.org/10.1103/PhysRevD.106.123503  

   Cao, Shuyang; Boyanovsky, Daniel (December 2022, Physical Review D)

   We study the non-equilibrium dynamics of a pseudoscalar axion-like particle (ALP) weakly coupled to degrees of freedom in thermal equilibrium by obtaining its reduced density matrix. Its time evolution is determined by the in-in effective action which we obtain to leading order in the (ALP) coupling but to \emph{all orders} in the couplings of the bath to other fields within or beyond the standard model. 

   more » « less
3. The Brownian transport map

   https://doi.org/10.1007/s00440-024-01286-0  

   Mikulincer, Dan; Shenfeld, Yair (May 2024, Probability Theory and Related Fields)

   Abstract Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual construction of such maps, however, is a non-trivial task and, so far, relies mostly on the theory of optimal transport. In this work, we take advantage of the infinite-dimensional nature of the Gaussian measure and construct a new transport map, based on the Föllmer process, which pushes forward the Wiener measure onto probability measures on Euclidean spaces. Utilizing the tools of the Malliavin and stochastic calculus in Wiener space, we show that this Brownian transport map is a contraction in various settings where the analogous questions for optimal transport maps are open. The contraction properties of the Brownian transport map enable us to prove functional inequalities in Euclidean spaces, which are either completely new or improve on current results. Further and related applications of our contraction results are the existence of Stein kernels with desirable properties (which lead to new central limit theorems), as well as new insights into the Kannan–Lovász–Simonovits conjecture. We go beyond the Euclidean setting and address the problem of contractions on the Wiener space itself. We show that optimal transport maps and causal optimal transport maps (which are related to Brownian transport maps) between the Wiener measure and other target measures on Wiener space exhibit very different behaviors. 

   more » « less
4. Settling dynamics of Brownian chains in viscous fluids

   https://doi.org/10.1103/PhysRevFluids.7.034303  

   Cunha, Lucas H.; Zhao, Jingjing; MacKintosh, Fred C.; Biswal, Sibani Lisa (March 2022, Physical Review Fluids)
5. Exact correlation functions in the Brownian Loop Soup

   https://doi.org/10.1007/JHEP07(2020)067  

   Camia, Federico; Foit, Valentino F.; Gandolfi, Alberto; Kleban, Matthew (July 2020, Journal of High Energy Physics)