Roland Bauerschmidt

I am a Professor of Probability in the Statistical Laboratory, part of 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

Teaching

The renormalisation group (IHES, March 2022)

[Past courses]

Other current items

Cambridge Probability Seminar (co-organiser)
Analysis, Quantum Fields, and Probability (co-organiser)
Probability and Mathematical Physics (associate editor)
Annals of Probability (associate editor)

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, stochastic dynamics, and supersymmetry in probability theory.

[More]

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

Log-Sobolev inequality for near critical Ising models R. Bauerschmidt, B. Dagallier Preprint
Log-Sobolev inequality for the φ⁴₂ and φ⁴₃ measures R. Bauerschmidt, B. Dagallier Preprint
The Discrete Gaussian model, II. Infinite-volume scaling limit at high temperature R. Bauerschmidt, J. Park, P.-F. Rodriguez Preprint
The Discrete Gaussian model, I. Renormalisation group flow at high temperature R. Bauerschmidt, J. Park, P.-F. Rodriguez Preprint
Percolation transition for random forests in d ≥ 3 R. Bauerschmidt, N. Crawford, T. Helmuth Preprint
The Coleman correspondence at the free fermion point R. Bauerschmidt, C. Webb J. Eur. Math. Soc., to appear
Maximum and coupling of the sine-Gordon field R. Bauerschmidt, M. Hofstetter Ann. Probab., 50, 455–508, (2022)
Random Spanning Forests and Hyperbolic Symmetry R. Bauerschmidt, N. Crawford, T. Helmuth, A. Swan Commun. Math. Phys., 381, 1223–1261, (2021)
Mean-field tricritical polymers R. Bauerschmidt, G. Slade Probab. Math. Phys., 1, 167–204, (2020)
Edge rigidity and universality of random regular graphs of intermediate degree R. Bauerschmidt, J. Huang, A. Knowles, H.-T. Yau Geom. Funct. Anal., 30, 693–769, (2020)
Log-Sobolev inequality for the continuum sine-Gordon model R. Bauerschmidt, T. Bodineau Comm. Pure Appl. Math., 74, 2064–2113, (2021)
Three-dimensional tricritical spins and polymers R. Bauerschmidt, M. Lohmann, G. Slade J. Math. Phys., 61, 033302, 30, (2020)
The geometry of random walk isomorphism theorems R. Bauerschmidt, T. Helmuth, A. Swan Ann. Inst. Henri Poincaré Probab. Stat., 57, 408–454, (2021)
Spectral Gap Critical Exponent for Glauber Dynamics of Hierarchical Spin Models R. Bauerschmidt, T. Bodineau Commun. Math. Phys., 373, 1167–1206, (2020)
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., 23, 841–1002, (2019)
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, 3375–3396, (2019)
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, 3019–3057, (2019)
Local Kesten-McKay law for random regular graphs R. Bauerschmidt, J. Huang, H.-T. Yau Commun. Math. Phys., 369, 523–636, (2019)
A very simple proof of the LSI for high temperature spin systems R. Bauerschmidt, T. Bodineau J. Funct. Anal., 276, 2582–2588, (2019)
Bulk eigenvalue statistics for random regular graphs R. Bauerschmidt, J. Huang, A. Knowles, H.-T. Yau Ann. Probab., 45, 3626–3663, (2017)
Local density for two-dimensional one-component plasma R. Bauerschmidt, P. Bourgade, M. Nikula, H.-T. Yau Commun. Math. Phys., 356, 189–230, (2017)
Local semicircle law for random regular graphs R. Bauerschmidt, A. Knowles, H.-T. Yau Comm. Pure Appl. Math., 70, 1898–1960, (2017)
Four-dimensional weakly self-avoiding walk with contact self-attraction R. Bauerschmidt, G. Slade, B.C. Wallace J. Stat. Phys., 167, 317–350, (2017) (Errata)
Finite-order correlation length for four-dimensional weakly self-avoiding walk and |φ|⁴ spins R. Bauerschmidt, G. Slade, A. Tomberg, B.C. Wallace Ann. Henri Poincaré, 18, 375–402, (2017) (Errata)
Critical two-point function of the 4-dimensional weakly self-avoiding walk R. Bauerschmidt, D.C. Brydges, G. Slade Commun. Math. Phys., 338, 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, 817–877, (2015) (Errata)
A renormalisation group method. III. Perturbative analysis R. Bauerschmidt, D.C. Brydges, G. Slade J. Stat. Phys., 159, 492–529, (2015) (Errata) (Code)
Structural stability of a dynamical system near a non-hyperbolic fixed point R. Bauerschmidt, D.C. Brydges, G. Slade Ann. Henri Poincaré, 16, 1033–1065, (2015) (Errata)
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., 157, 692–742, (2014) (Errata)
Fluctuations in a kinetic transport model for quantum friction R. Bauerschmidt, W. Roeck, J. Fröhlich J. Phys. A, 47, 275003, 15, (2014)
A simple method for finite range decomposition of quadratic forms and Gaussian fields R. Bauerschmidt Probab. Theory Related Fields, 157, 817–845, (2013)

Book

Introduction to a renormalisation group method R. Bauerschmidt, D.C. Brydges, G. Slade Lecture Notes in Mathematics, 2242, xii+281, (2019)

Proceedings and lecture notes

Spin systems with hyperbolic symmetry: a survey R. Bauerschmidt, T. Helmuth Proceedings ICM 2022
Renormalisation group analysis of 4D spin models and self-avoiding walk R. Bauerschmidt, D.C. Brydges, G. Slade Proceedings ICMP 2015
Lectures on self-avoiding walks R. Bauerschmidt, H. Duminil-Copin, J. Goodman, G. Slade Clay Math. Proc., 15, 395–467, (2012)

Miscellaneous

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

Acknowledgement

I gratefully acknowledge funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 851682 SPINRG).