There are two main directions of my interests: 1) the large deviations in queuing systems, 2) Gibbs random fields. In the collaborations with R. Dobrushin a large deviation principle was proved for processes with independent increments. The result has a form applicable to queuing systems. Tandem queuing systems were studied by this result. The bottle neck effect was proved under a large delay in the tandem system. The large deviations of different systems were studied as well. In the collaborations with R. Dobrushin a criterium of the Gibbs state uniqueness for non-compact spin spaces was obtained. The result was applied to studies of the uniqueness region of a non-ideal gas state. Some works are devoted to applications of the Gibbs field theory to the image processing.
Main publications:
E. Pechersky. The Peierls Condition (or GPS Condition) Is Not Always Satisfied // Sel. Math. Sov., 3, 1, 1983/84, 87–91.
F. I. Karpelevich, E. A. Pechersky, Yu. M. Suhov. A Phase Transition for Hyperbolic branching processes // Commun. Math. Phys., 195, 627–642, 1998.
F. Tupin, H. Maitre, J. F. Mangin, J. M. Nicolas, E. Pechersky. Detection of Linear Feature in SAR Images: Application to Road Network Extraction // IEEE Transactions on Geoscience and Remote Sensing, 36, 2, 1998, 434–453.
E. Pechersky, Yu. Zhukov. Uniqueness of Gibbs State for Non-Ideal Gas in ${\bf R}^d$: the case of pair potentials // J. Stat. Phys. 97, 1/2, 1999, 145–172.
