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Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits

- S. Smirnov
- Mathematics
- 1 August 2001

Towards conformal invariance of 2D lattice models

- S. Smirnov
- Mathematics, Physics
- 31 July 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… Expand

Universality in the 2D Ising model and conformal invariance of fermionic observables

- Dmitry Chelkak, S. Smirnov
- Mathematics, Physics
- 11 October 2009

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… Expand

Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model

- S. Smirnov
- Mathematics, Physics
- 31 July 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… Expand

CRITICAL EXPONENTS FOR TWO-DIMENSIONAL PERCOLATION

- S. Smirnov, W. Werner
- Mathematics
- 18 September 2001

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… Expand

The connective constant of the honeycomb lattice equals 2+2

- S. Smirnov
- Mathematics
- 2012

We provide the first mathematical proof that the connective constant of the hexagonal lattice is equal to √ 2 + √ 2. This value has been derived nonrigorously by B. Nienhuis in 1982, using Coulomb… Expand

Discrete Complex Analysis and Probability

- S. Smirnov
- Mathematics
- 30 September 2010

We discuss possible discretizations of complex analysis and some of their applications to probability and mathematical physics, following our recent work with Dmitry Chelkak, Hugo Duminil-Copin and… Expand

Harmonic Measure and SLE

- D. Beliaev, S. Smirnov
- Mathematics
- 11 January 2008

In this paper we study the multifractal structure of Schramm’s SLE curves. We derive the values of the (average) spectrum of harmonic measure and prove Duplantier’s prediction for the multifractal… Expand

The energy density in the planar Ising model

- C. Hongler, S. Smirnov
- Physics
- 16 August 2010

We study the critical Ising model on the square lattice in bounded simply connected domains with + and free boundary conditions. We relate the energy density of the model to a discrete fermionic… Expand

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