Fredrik Viklund

Research interests

My main areas of interest lie in complex analysis, probability, and mathematical physics, and especially problems where these areas meet. I am currently working on questions concerning Coulomb gases in the plane, the Loewner energy, Hele-Shaw flows, and lattice Yang-Mills theories.

Other topics of (past and present) interest are fine geometric properties of Schramm-Loewner evolution (SLE) curves; scaling limits of critical lattice models; Laplacian growth and aggregation models; analytic and probabilistic aspects of conformal field theory. 

Papers

• Planar Coulomb gas on a Jordan arc at any temperature

With K. Courteaut, K. Johansson

[arXiv]

• A current expansion for Ising lattice gauge theory

With M. P. Forsström

[arXiv] (Not for publication.)

• Competitive Hele-Shaw flow and quadratic differentials
  With D. Witt Nyström
  [arXiv]

• Coulomb gas and the Grunsky operator on a Jordan domain with corners
  With K. Johansson
  [arXiv]

• Free energy and quark potential in Ising lattice gauge theory via cluster expansion
  With M. P. Forsström

Int. Math. Res. Not. (IMRN) 2025:12 (2025).
[arXiv]

• Wilson lines in the lattice Higgs model at strong coupling
  With M. P. Forsström, J. Lenells
  Ann. Appl. Probab. 35: 1 (2025).
  [arXiv]

• Percolation for two-dimensional excursion clouds and the discrete Gaussian free field
  With A. Drewitz, O. Elias, A. Prevost, J. Tykesson
  Electron. J. Probab. 29 (2024)
  [arXiv]

• The Loewner-Kufarev Energy and Foliations by Weil-Petersson Quasicircles
  With Y. Wang
  Proc. London Math. Soc. 128:2 (2024)
  [arXiv]

• Wilson loops in the abelian lattice Higgs model
  With M. P. Forsström, J. Lenells
  Probability and Mathematical Physics (PMP) 4 (2) (2023)
  [arXiv]

• Wilson loops in finite Abelian lattice gauge theories
  With M. P. Forsström, J. Lenells
  Ann. Inst. Henri Poincaré 58 (4) 2129-2164 (2022)
  [arXiv]

• Conformal Field Theory at the Lattice Level: Discrete Complex Analysis and Virasoro Structure
  With C. Hongler, K. Kytola.
  Comm. Math. Phys. 395 1--58 (2022)
  [arXiv] [Journal]

• Convergence of loop-erased random walk in the natural parametrization
  With G. F. Lawler.
  Duke Math. J. 170 (10) (2021)
  [arXiv] [Journal]

• The Loewner difference equation and convergence of loop-erased random walk
  With G. F. Lawler.
  ALEA 19 (2022)
  [Journal]

• Dimensions of two-valued sets via imaginary chaos
  With L. Schoug, A. Sepulveda
  Int. Math. Res. Not. (IMRN) 2022 (5) (2022)
  [arXiv] [Journal]

• Remarks on the regularity of quasislits
  With L. Schoug, A. Shekhar
  Ann. Acad. Sci. Fenn. Math 46 (1) (2021)
  [arXiv] [Journal]

• Interplay between Loewner and Dirichlet energies via conformal welding and flow-lines
  With Y. Wang
  Geom. Funct. Anal. (GAFA) 30 289–321 (2020)
  [arXiv] [Journal]

• Asymptotic analysis of Dotsenko-Fateev integrals
  With J. Lenells
  Ann. Henri Poincaré 20 (11) 3799-3848 (2019)
  [arXiv] [Journal]

• Schramm's formula and the Green's function for multiple SLE
  With J. Lenells
  J. Stat. Phys. 176 (4) 873–931 (2019)
  [arXiv]

• Transition probabilities for infinite two-sided loop-erased random walks
  With C. Benes, G. F. Lawler.
  Electron. J. Probab. 24 Paper no 139, 22p (2019).
  [arXiv]

• One-dimensional scaling limits in a planar Laplacian random growth model
  With A. Sola, A. Turner.
  Comm. Math. Phys. 371 (1) (2019)
  [arXiv] [Journal]

• Convergence of radial loop-erased random walk in the natural parametrization
  With G. F. Lawler
  [arXiv]

• A dimension spectrum for SLE boundary collisions
  With T. Alberts, I. Binder.
  Comm. Math. Phys 348 (1) 273–298, (2016)
  [arXiv]

• Scaling limit of the loop-erased random walk Green's function
  With C. Benes, G. F. Lawler.
  Probab. Theory. Related Fields, 166 (1-2), 271–319 (2016)
  [arXiv]

• Small particle limits in a regularized Laplacian random growth model
  With A. Sola, A. Turner.
  Comm. Math. Phys. 334 (1), 331-366, (2015)
  [arXiv] [Simulations]

• Convergence rates for loop-erased random walk and other Loewner curves
  Ann. Probab. 43 (1), 119-165 (2015)
  [arXiv]

• On the continuity of SLE(k) in k
  With S. Rohde, C. Wong.
  Probab. Theory Related Fields 159 (3), 413-433 (2014)
  [arXiv]

• Some remarks on SLE bubbles and Schramm's two-point observable
  With D. Beliaev.
  Comm. Math. Phys. 320 (2), 379-394 (2013)
  [arXiv]

• Almost sure multifractal spectrum for the tip of an SLE curve
  With G. F. Lawler.
  Acta Math. 209, 265-322 (2012)
  [arXiv]

• On the rate of convergence of loop-erased random walk to SLE(2)
  With C. Benes and M. Kozdron.
  Comm. Math. Phys. 308 (2), 307-354 (2013)
  [arXiv]

• Optimal Holder exponent for the SLE path
  With G. F. Lawler.
  Duke Math. J. 159 (3), 351-383 (2011)
  [Journal] [arXiv]

• Scaling limits of anisotropic Hastings-Levitov clusters
  With A. Sola and A. Turner.
  Ann. Inst. Henri Poincaré  48, 235-257 (2012)
  [Journal] [arXiv]

• On the scaling limit of loop-erased random walk excursion
  Ark. Mat. 50 (2) (2012)
  [Journal]

• Random Loewner Chains
  Doctoral Thesis from KTH Royal Institute of Technology, April 2010.

• Rescaled Levy-Loewner hulls and random growth
  With A. Sola.
  Bull. Sci. Math. 133, 238-256 (2009)
  [Journal] [arXiv]

Contact

Email: frejo --at-- kth.se

Mailing Address: 

Fredrik Viklund

Department of Mathematics, KTH Royal Institute of Technology

100 44 Stockholm, Sweden

Office:

Room 3527, Department of Mathematics, KTH
Drottning Kristinas Vag 25

Picture by Magnus Bergstrom/KAW