Roland Bauerschmidt

Reader, Statistical Laboratory, DPMMS, 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

Markov Chains (Cambridge, Michaelmas 2020)
Applied Probability (Cambridge, Lent 2021)

[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

The Coleman correspondence at the free fermion point R. Bauerschmidt, C. Webb Preprint
Maximum and coupling of the sine-Gordon field R. Bauerschmidt, M. Hofstetter Preprint
Random spanning forests and hyperbolic symmetry R. Bauerschmidt, N. Crawford, T. Helmuth, A. Swan Commun. Math. Phys., to appear
Mean-field tricritical polymers R. Bauerschmidt, G. Slade Prob. Math. Phys., to appear
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., to appear
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., to appear
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

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, 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).