Summary
In this paper we compute the Fourier transform of the free energy of the percolation process. We apply the Fourier transform technique to rederive a result of Aizenman-Kesten-Newman that the derivative of the free energy is continuous.
References
Aizenman, M., Kesten, H., Newman, C.M.: Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. Comm. Math. Phys. 111, 505–531 (1987)
Kesten, H.: Percolation theory for mathematicians. Boston: Birkhauser 1982
Author information
Authors and Affiliations
Additional information
This research was supported by the Air Force Office of Scientific Research, Grant No. F49620 85 C0144
Part of this work was also carried out at The University of Mississippi, Department of Mathematics, University, MS 38677, USA
Rights and permissions
About this article
Cite this article
Nguyen, B.G. Fourier transform of the percolation free energy. Probab. Th. Rel. Fields 78, 165–168 (1988). https://doi.org/10.1007/BF00322016
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00322016
Keywords
- Fourier
- Free Energy
- Fourier Transform
- Stochastic Process
- Probability Theory