I am a Ph.D. student in mathematics in the
Probability Theory Group at the University of British Columbia.
University of British Columbia
Department of Mathematics
121-1984 Mathematics Road
Vancouver, BC, V6T 1Z2, Canada
E-mail address: brt at the same domain as this webpage
In Fall 2013, I will be at the Institute for Advanced Study, Princeton.
Research in mathematics
My mathematical research interest is in probability theory, analysis, and their applications;
in particular, I'm interested in multiscale and renormalization group methods in the context of random fields
and self-interacting random walks.
My Ph.D. supervisors are
I have obtained my B.Sc. and M.Sc. degrees
in physics from ETH Zürich. My master's thesis was supervised
by Jürg Fröhlich and Wojciech de Roeck.
Current projects (in progress)
The following projects are ongoing together with David Brydges and Gordon Slade,
and related to a bigger project of these two authors in which they develop a
renormalization group method to study field theories with quartic self-interaction on the Euclidean lattice.
Logarithmic corrections to the scaling behavior of four dimensional weakly self-avoiding walks.
The ultimate goal is to establish that the extent of four dimensional weakly self-avoiding walks of length t grows asymptotically like
t1/2 |log t|1/8. This is in contrast to the simple random walk and the self-avoiding walk in
dimensions strictly above four which both grow like t1/2, and the self-avoiding walk in dimensions strictly below
four which is conjectured (but not known rigorously) to grow like tα with α > 1/2.
More immediate goals are to prove such asymptotic behavior in
averaged form, e.g. that the susceptibility and the correlation lengths of order p have the corresponding
divergences as the critical point is approached.
Linear polymers with self-attraction in dimension four and higher.
The self-avoiding walk is a basic model for a long molecule chain in a good solution. The self-avoidance constraint models the
volume effect of the polymer. In a poor solution, there are two competing forces, a repelling one that models the
volume effect of the polymer, and an attractive force that accounts for the fact that the polymer tries to avoid contact
with the solution.
We show that the renormalization group method for the weakly self-avoiding walk developed by Brydges and Slade
can be extended to show that the two-point function has mean-field behavior in a region of the extended phase of the polymer.
Completed manuscripts (preprints)
Structural stability of a dynamical system near a non-hyperbolic fixed point
R. Bauerschmidt, D.C. Brydges, and G. Slade
Revised version will appear in Annales Henri Poincaré.
A simple method for finite range decomposition of quadratic forms and Gaussian fields
Accepted for publication in Probability Theory and Related Fields.
Lectures on Self-Avoiding Walks
R. Bauerschmidt, H. Duminil-Copin, J. Goodman, and G. Slade
Probability and Statistical Physics in Two and More Dimensions, Clay Mathematics Proceedings, vol. 15, Amer. Math. Soc., 2010, pp. 395-476
Finite range decomposition of Green's functions
McGill University Analysis Seminar
My favorite author is Paul Auster.