Interests:  Statistical Mechanics, Quantum Field Theory, Functional Integration, Probability

A large part of theoretical physics is built around the “functional integral” formulation of quantum field theory.  These functional integrals are defined in the sense of formal power series (renormalised perturbation theory).  It is commonly thought by mathematicians, that no precise definition that is useful for rigorous analysis is within sight.  However the renormalization group (RG), as pioneered by Ken Wilson (Nobel prize in Physics, 1982),  is  a program for defining functional integrals and studying the remarkable  range of phenomena contained within them, in particular, renormalisation, scaling limits and the phase transitions of statistical mechanics. In these cases the theory of Gaussian measures on spaces of functions or distributions is the starting point and it is a good starting point for any problem which is "close to real Gaussian".   This allows a surprising large  range of applications.  My interests in  recent years have been in applications to  self-avoiding walk in four dimensions.  It is possible to express self-avoiding walk and other systems in terms of nearly Gaussian integrals with supersymmetry which can be studied by RG.  My colleague Joel Feldman is also using RG in the context of condensed matter physics.  His work leads to nearly Gaussian integrals with complex densities. These integrals are not so well understood but they appear in any problem where time has a direction, for example random walk in a random environment which is not symmetric.

Roland Bauerschmidt, Decomposition of free fields and structural
stability of dynamical systems for renormalization group analysis, PhD Thesis 2013,

Roland Bauerschmidt, David C. Brydges, Gordon Slade, Structural stability of a dynamical system near a non-hyperbolic fixed point

David Brydges and Thomas Spencer, Fluctuation estimates for sub-quadratic gradient field actions, Journal of Mathematical Physics (Vol.53, Issue 9, 2012): URL:, DOI: 10.1063/1.4747194

D.C. Brydges, A. Dahlqvist and G. Slade. The strong interaction limit of continuous-time weakly self-avoiding walk. In Probability in Complex Physical Systems: In Honour of Erwin Bolthausen and Jürgen Gärtner, eds. J-D. Deuschel et al., Springer Proceedings in Mathematics 11:275--287, (2012)
PDF file

D. Brydges and G. Slade. Renormalisation group analysis of weakly self-avoiding walk in dimensions four and higher. Revised April 27, 2010. In Proceedings of the International Congress of Mathematicians, 2010, eds. R. Bhatia et al., Volume 4, pp. 2232--2257, World Scientific, (2010).  PDF file

D.C. Brydges, J.Z. Imbrie, G. Slade. Functional integral representations for self-avoiding walk. Probability Surveys, 6:34--61, (2009).  PDF file

Lectures at the 2007 Park City Summer School   (Corrections welcomed).

Statistical Mechanics Edited by: Scott Sheffield, Massachusetts Institute of Technology, Cambridge, MA, and Thomas Spencer, Institute for Advanced Study, Princeton, NJ

Brydges, David and Talarczyk, Anna,  Finite range decompositions of positive-definite functions,
Journal of Functional Analysis, Volume 236, Issue 2, 15 July 2006, Pages 682-711

David C.Brydges, G.Guadagni, P.K.Mitter
Finite range Decomposition of Gaussian Processes JSP  2004, 115,  pages {415--449},
D. C. Brydges, P. K. Mitter, B. Scoppola.  CRITICAL (Phi^{4}_{3,/epsilon})  Communications in Mathematical Physics, 240, 2003, pages  281--327

On Self Avoiding Walk and related problems (Applications of functional integration and supersymmetry) Lectures sponsored by PIMS

David C. Brydges, John Z. Imbrie.  Green's Function for a Hierarchical Self-Avoiding Walk in Four Dimensions,  Communications in Mathematical Physics, 239, 2003, pages 549--584

David C. Brydges, John Z. Imbrie.  End-to-end Distance from the Green's Function for a Hierarchical Self-Avoiding Walk
in Four Dimension Communications in Mathematical Physics,  239, 2003, pages 523--547

David C. Brydges, John Z. Imbrie.  Dimensional Reduction Formulas for Branched Polymer Correlation Functions,  Journal of Statistical Physics, 110,  2003, pages 503--518

David C. Brydges, John Z. Imbrie Branched Polymers and Dimensional Reduction,     Annals of Mathematics,
2003,  158,  pages 1019­-103

On Coulomb Systems (Application of Gaussian Functional Integration)
David C. Brydges, Ph. A. Martin.    Coulomb systems at low density, Journal of Statistical Physics,  96, 1999, 1163--1330

Combinatoric Result

A. Abdesselam and D. C. Brydges, Cramer's Rule and Loop Ensembles
This is a review of a result of G.X. Viennot which we think is important for statistical mechanics.

A day in the life  here.