# Hadamard’s formula and couplings of SLEs with free field

@article{Izyurov2010HadamardsFA, title={Hadamard’s formula and couplings of SLEs with free field}, author={Konstantin Izyurov and Kalle Kyt{\"o}l{\"a}}, journal={Probability Theory and Related Fields}, year={2010}, volume={155}, pages={35-69} }

The relation between level lines of Gaussian free fields (GFF) and SLE4-type curves was discovered by O. Schramm and S. Sheffield. A weak interpretation of this relation is the existence of a coupling of the GFF and a random curve, in which the curve behaves like a level line of the field. In the present paper we study these couplings for the free field with different boundary conditions. We provide a unified way to determine the law of the curve (i.e. to compute the driving process of the… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 13 REFERENCES

## M

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## SLE and the free field: Partition functions and couplings

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Random Loewner Chains in Riemann Surfaces

VIEW 1 EXCERPT