Stochastic processes and conformal invariance

Abstract

We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent $z=1$. The events that occur are adsorption, which is local, and desorption which is non-local and may take place over regions of the order of the system size. In the thermodynamic limit, the time dependence of the system is given by characters of the $c=0$ conformal field theory of percolation. This implies in a rigorous way a connection between CFT and stochastic processes. The finite-size scaling behavior of the average height, interface width and other observables are obtained. The avalanches produced during desorption are analyzed and we show that the probability distribution of the avalanche sizes obeys finite-size scaling with new critical exponents.

4 pages, 6 figures, revtex4. v2: change of title and minor corrections

References in corpus (4)

• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• Temperley-Lieb Stochastic Processes
• World Sheet Logarithmic CFT in AdS Strings, Ghost-Matter Mixing and M-theory

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• Correlations in the $n\to 0$ limit of the dense O(n) loop model
• Critical behavior in a non-local interface model
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