Quasisymmetric distortion spectrum (2009)
Prause, István, Smirnov, Stanislav
We give improved bounds for the distortion of the Hausdorff dimension under quasisymmetric maps in terms of the dilatation of their quasiconformal extension. The sharpness of the estimates remains an...
Universality in the 2D Ising model and conformal invariance of fermionic observables (2009)
Chelkak, Dmitry, Smirnov, Stanislav
It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no...
Off-critical lattice models and massive SLEs (2009)
Makarov, Nikolai, Smirnov, Stanislav
We suggest how versions of Schramm's SLE can be used to describe the scaling limit of some off-critical 2D lattice models. Many open questions remain.
Critical percolation: the expected number of clusters in a rectangle (2009)
Hongler, Clément, Smirnov, Stanislav
We show that for critical site percolation on the triangular lattice two new observables have conformally invariant scaling limits. In particular the expected number of clusters separating two pairs...
Critical percolation in the plane (2009)
We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolation-related quantities are harmonic conformal invariants, and calculate...
Dimension of quasicircles (2009)
We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala's...
Discrete complex analysis on isoradial graphs (2008)
Chelkak, Dmitry, Smirnov, Stanislav
We study discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones. Along with discrete analogues of several classical results, we prove uniform...
Non-uniform hyperbolicity in complex dynamics (2008)
Graczyk, Jacek, Smirnov, Stanislav
We study rational functions satisfying summability conditions - a family of weak conditions on the expansion along the critical orbits. Assuming their appropriate versions, we derive many nice...
Towards conformal invariance of 2D lattice models (2007)
Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but...
Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model (2007)
We construct discrete holomorphic observables in the Ising model at criticality and show that they have conformally covariant scaling limits (as mesh of the lattice tends to zero). In the sequel...
Critical exponents for two-dimensional percolation (2006)
Smirnov, Stanislav, Werner, Wendelin
We show how to combine Kesten's scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov's proof...
Critical exponents for two-dimensional percolation (2001)
Smirnov, Stanislav, Werner, Wendelin
We show how to combine Kesten's scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov's proof...
Symbolic dynamics and Collet-Eckmann conditions (2000)
We prove that unicritical polynomials with metrically generic combinatorics of the critical orbit satisfy the Collet-Eckmann conditions. Here metrically generic means except for a set of Hausdorff...