Roland Bauerschmidt

I am a University Lecturer (equivalent of Assistant Professor) in the Statistical Laboratory, in the Department of Pure Mathematics and Mathematical Statistics, at the University of Cambridge.

E-mail: rb812 [at] cam.ac.uk

Office: D1.19
Phone: +44 1223 766806

Address:
University of Cambridge
Centre for Mathematical Sciences
Wilberforce Road
Cambridge, CB3 0WB, UK

Current teaching

Other current items

Probability Seminar
New journal Probability and Mathematical Physics

Research interests

My mathematical research interests are in probability theory and analysis, in particular in their applications to statistical mechanics.

I am particularly interested in spin systems and phase transitions, self-avoiding walks, random matrices, renormalization, dynamics, and supersymmetry.

Background

Before coming to Cambridge, I was post-doc at Harvard University and the Institute for Advanced Study. I received by PhD from the University of British Columbia and my undergraduate degrees from ETH Zurich. My advisers and post-doc mentors were David Brydges, Jürg Fröhlich, Wojciech de Roeck, Gordon Slade, Tom Spencer and Horng-Tzer Yau.

Publications

Random spanning forests and hyperbolic symmetry R. Bauerschmidt, N. Crawford, T. Helmuth, A. Swan Preprint
Mean-field tricritical polymers R. Bauerschmidt, G. Slade Preprint
Edge rigidity and universality of random regular graphs of intermediate degree R. Bauerschmidt, J. Huang, A. Knowles, H.-T. Yau Preprint
Log-Sobolev inequality for the continuum Sine-Gordon model R. Bauerschmidt, T. Bodineau Preprint
Three-dimensional tricritical spins and polymers R. Bauerschmidt, M. Lohmann, G. Slade Preprint
The geometry of random walk isomorphism theorems R. Bauerschmidt, T. Helmuth, A. Swan Preprint
Dislocation lines in three-dimensional solids at low temperature R. Bauerschmidt, D. Conache, M. Heydenreich, F. Merkl, S.W.W. Rolles Ann. Henri Poincaré, 20, no. 9, 3019–3057, (2019)
Spectral gap critical exponent for Glauber dynamics of hierarchical spin models R. Bauerschmidt, T. Bodineau Commun. Math. Phys., to appear
Dynkin isomorphism and Mermin-Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump process R. Bauerschmidt, T. Helmuth, A. Swan Ann. Probab., 47(5):3375-3396, (2019)
A very simple proof of the LSI for high temperature spin systems R. Bauerschmidt, T. Bodineau J. Funct. Anal., Vol. 276, 8, 2582-2588, (2019)
Four-dimensional weakly self-avoiding walk with contact self-attraction R. Bauerschmidt, G. Slade, B. Wallace J. Stat. Phys., 167(2):317–350, (2017)
Local Kesten-McKay law for random regular graphs R. Bauerschmidt, J. Huang, H.-T. Yau Commun. Math. Phys., 369, no. 2, 523–636, (2019)
The two-dimensional Coulomb plasma: quasi-free approximation and central limit theorem R. Bauerschmidt, P. Bourgade, M. Nikula, H.-T. Yau Adv. Theor. Math. Phys., Vol. 23, No. 4, pp. 841-1002, (2019)
Finite-order correlation length for 4-dimensional weakly self-avoiding walk and |φ|⁴ spins R. Bauerschmidt, G. Slade, A. Tomberg, B.C. Wallace Ann. Henri Poincaré, 18(2):375–402, (2017)
Local density for two-dimensional one-component plasma R. Bauerschmidt, P. Bourgade, M. Nikula, H.-T. Yau Commun. Math. Phys., 356(1):189–230, (2017)
Bulk eigenvalue statistics for random regular graphs R. Bauerschmidt, J. Huang, A. Knowles, H.-T. Yau Ann. Probab., 45(6A):3626–3663, (2017)
Local semicircle law for random regular graphs R. Bauerschmidt, A. Knowles, H.-T. Yau Comm. Pure Appl. Math., 70(10):1898–1960, (2017)
Scaling limits and critical behaviour of the 4-dimensional n-component |φ|⁴ spin model R. Bauerschmidt, D.C. Brydges, G. Slade J. Stat. Phys., Vol. 157, 4-5, 692-742, (2015) Special issue in memory of Kenneth Wilson (Nobel Prize in Physics 1982).
Critical two-point function of the 4-dimensional weakly self-avoiding walk R. Bauerschmidt, D.C. Brydges, G. Slade Commun. Math. Phys., 338(1):169–193, (2015)
Logarithmic correction for the susceptibility of the 4-dimensional weakly self-avoiding walk: a renormalisation group analysis R. Bauerschmidt, D.C. Brydges, G. Slade Commun. Math. Phys., 337(2):817–877, (2015)
A renormalisation group method. III. Perturbative analysis R. Bauerschmidt, D.C. Brydges, G. Slade J. Stat. Phys., 159:492–529, (2015) [→Code]
Fluctuations in a kinetic transport model for quantum friction R. Bauerschmidt, W. de Roeck, J. Fröhlich J. Phys. A: Math. Theor., 47 275003, (2014)
Structural stability of a dynamical system near a non-hyperbolic fixed point R. Bauerschmidt, D.C. Brydges, G. Slade Ann. Henri Poincaré, Vol. 16, 4, 1033-1065, (2015)
A simple method for finite range decomposition of quadratic forms and Gaussian fields R. Bauerschmidt Probab. Theory Related Fields, Vol. 157, 3-4, 817-845, (2013)

Book

Introduction to a renormalisation group method R. Bauerschmidt, D.C. Brydges, G. Slade Lecture Notes in Mathematics, volume 2242, Springer (2019).

Proceedings and lecture notes

Renormalisation group analysis of 4D spin models and self-avoiding walk R. Bauerschmidt, D.C. Brydges, G. Slade Proceedings ICMP, Santiago de Chile, July 2015
Lectures on Self-Avoiding Walks R. Bauerschmidt, H. Duminil-Copin, J. Goodman, and G. Slade Clay Mathematics Proceedings, Vol. 15, Amer. Math. Soc., 395-476, (2010).

» Show all publications

Links previously here

Harvard Random Matrix and Probability Seminar (Harvard, 2015/2016)
MATH 253x Spin Systems (Harvard, Spring 2016)
Linear Analysis (Cambridge, Michaelmas 2016)
Linear Analysis (Cambridge, Michaelmas 2017)
Stochastic Calculus and Applications (Cambridge, Lent 2018)
Spin Systems: Discrete and Continuous (Darmstadt Spring School, March 2018)
Summer School on Current Topics in Mathematical Physics (Fields Institute, July 2018)
Linear Analysis (Cambridge, Michaelmas 2018)
Stochastic Calculus and Applications (Cambridge, Lent 2019)

Miscellaneous

My favourite author is Paul Auster. My PGP public key.