School of Mathematical and Statistical Sciences

Nicolas Lanchier
School of Mathematical
and Statistical Sciences
Arizona State University
Tempe, AZ 85287-1804

Office: PSA 628
Email: lanchier@math.asu.edu
Phone number: 480-965-3870

Curriculum Vitae
Ph.D. dissertation:
Multicolor particle systems

Numerical simulations

The file GTK.zip contains the 19 numerical simulations described below, and a makefile which will allow you to compile the different programs. To create the executable file, just type: make file_name. To run the executable file, then type: ./file_name. The compilation requires the installation of GTK+ included in recent versions of Linux. The XFIG button created by running the programs will allow you to obtain pictures at the XFIG format.

Voter model - VMD-1 & VMD-2.
  • Clifford, P. and Sudbury, A. (1973). A model for spatial conflict. Biometrika 60 581-588.
  • Holley, R. A. and Liggett, T. M. (1975). Ergodic theorems for weakly interacting infinite systems and the voter model. Ann. Probab. 3 643-663.
  • Cox, J. T and Griffeath, D. (1986). Diffusive clustering in the two-dimensional voter model. Ann. Probab. 14 347-370.
Basic and multitype contact processes - MCP-1 & MCP-2.
  • Harris, T. E. (1974). Contact interactions on a lattice. Ann. Probab. 2 969-988.
  • Neuhauser, C. (1992). Ergodic theorems for the multitype contact process. Probab. Theory Related Fields 91 467-506.
Spatial epidemics with removal & partial immunization - EWR-2.
  • Cox, J. T. and Durrett, R. (1988). Limit theorems for the spread of epidemics and forest fires. Stochastic Process. Appl. 30 171-191.
  • Durrett, R. and Neuhauser, C (1991). Epidemics with recovery in d = 2. Ann. Appl. Probab. 1 189-206.
  • van den Berg, J., Grimmett, G. R. and Schinazi, R. B. (1998). Dependent random graphs and spatial epidemics. Ann. Appl. Probab. 8 317-336.
  • Stacey, A. M. (2003). Partial immunization processes. Ann. Appl. Probab. 13 669-690.
Stepping stone model (cluster size = 8) - SSM-1 & SSM-2.
  • Kimura, M. and Weiss, G. H. (1964). The stepping stone model of population structure and the decrease of genetic correlation with distance. Genetics 49 561-576.
  • Cox, J. T. and Durrett, R. (2002). The stepping stone model: new formulas expose old myths. Ann. Appl. Probab. 12 1348-1377.
Spatially explicit Lotka-Volterra model - LVM-1 & LVM-2.
  • Neuhauser, C and Pacala, S. W. (1999). An explicitly spatial version of the Lotka-Volterra model with interspecific competition. Ann. Appl. Probab., 9 1226-1259.
Multitype Richardson model - MRM-2.
  • Haggstrom, O. and Pemantle, R. (1998). First passage percolation and a model for competing spatial growth. J. Appl. Probab. 35 683-692.
  • Haggstrom, O. and Pemantle, R. (2000). Absence of mutual unbounded growth for almost all parameter values in the two-type Richardson model. Stochastic Process. Appl. 90 207-222.
  • Kordzakhia, G. and Lalley, S. P.. (2005). A two-species competition model on Zd. Stochastic Process. Appl. 115 781-796.
Ecological succession model - ESM-2.
  • Lanchier, N. (2005). Phase transitions and duality properties of a successional model. Adv. in Appl. Probab. 37 265-278.
Multitype contact process with frozen sites - MFS-2.
  • Lanchier, N. (2005). A multitype contact process with frozen sites: a spatial model of allelopathy. J. Appl. Probab. 42 1109-1119.
Static-host model - SHM-2.
  • Lanchier, N. and Neuhauser, C. (2006). A spatially explicit model for competition among specialists and generalists in a heterogeneous environment. Ann. Appl. Probab. 16 1385-1410.
Dynamic-host models - DHM-2a, DHM-2b & BDHM-2.
  • Lanchier, N. and Neuhauser, C. (2006). Stochastic spatial models of host-pathogen and host-mutualist interactions. I. Ann. Appl. Probab. 16 448-474.
  • Lanchier, N. and Neuhauser, C. (2010). Stochastic spatial models of host-pathogen and host-mutualist interactions. II. Preprint.
  • Durrett, R. and Lanchier, N. (2008). Coexistence in host-pathogen systems. Stochastic Process. Appl. 118 1004-1021.
Individual and cluster recovery processes - IRP-2.
  • Schinazi, R. B. (2002). On the role of social clusters in the transmission of infectious diseases. Theoret. Pop. Biol. 61 163-169.
  • Belhadji, L. and Lanchier, N. (2006). Individual versus cluster recoveries within a spatially structured population. Ann. Appl. Probab. 16 403-422.
Two-scale contact process - 2CP-2.
  • Belhadji, L. and Lanchier, N. (2008). Two-scale contact process and effects of habitat fragmentation on metapopulations. Markov Process. Related Fields. 14 487-514.
  • Lanchier, N. (2010). Two-scale multitype contact process: coexistence in spatially explicit metapopulations. Preprint.
Non-Mendelian diploid model - SNM-2.
  • Lanchier, N. and Neuhauser, C. (2009). Spatially explicit non-Mendelian diploid model. Ann. Appl. Probab. 19, 1880-1920.