# Janko Gravner

**Regular Faculty****Probability**

Ph.D., 1991, University of Wisconsin, Madison**Refereed publications:** Via Math Reviews

**Web Page: ** http://www.math.ucdavis.edu/~gravner/

Email: gravner@math.ucdavis.edu

Office: MSB 3210

Phone: 752-0825

### Research

Professor Gravner studies deterministic and random cellular automata. These mathematical objects describe configurations which evolve by a repeated update of a local rule. Cellular automata have been used to model many natural phenomena and have offered insights into fundamental organizational principles in many scientific fields. From a more abstract perspective, cellular automata are a suitable tool used to characterize and catalog local dynamics which generate a prescribed global phenomenon. An important feature of this field is the interplay between rigorous mathematical analysis and large–scale computation, data analysis,and visualization.

### Selected publications

**[1]**Gravner, J., and J. Quastel. "Internal DLA and the Stefan problem,"

*Annals of Probability*,

**28**(4):1528-1562, (2000), Full Text.

**[2]** Gravner, J., and D. Griffeath. "Random growth models with polygonal shapes," *Annals of Probability*, **34**(1):181-218, (2006),
Full Text.

**[3]** Gravner, J., Pitman, D., and S. Gavrilets. "Percolation on fitness landscapes: effects of correlation, phenotype, and incompatibilities," *Journal of Theoretical Biology*, **248**(4):627-645, (2007),
Full Text.

**[4]** Gravner, J., and D. Griffeath. "Modeling snow-crystal growth: a three-dimensional approach," *Physical Review E*, **79**: 011604, 1-18, (2009),
Full Text.

**[5]** Gravner, J., and D. Griffeath. "Asymptotic densities for Packard *Box* rules," *Nonlinearity*, **22**(8):1817-1846, (2009),
Full Text.

*Last updated: 2012-05-08*