Numerical estimates for arm exponents and the acceptance profile in two-dimensional invasion percolation

dc.contributor.advisor Damron, Michael
dc.contributor.author Li, Jiaheng
dc.contributor.committeeMember Houdré, Christian
dc.contributor.committeeMember Tikhomirov, Konstantin
dc.contributor.department Mathematics
dc.date.accessioned 2020-05-20T17:02:01Z
dc.date.available 2020-05-20T17:02:01Z
dc.date.created 2020-05
dc.date.issued 2020-05-05
dc.date.submitted May 2020
dc.date.updated 2020-05-20T17:02:01Z
dc.description.abstract The main object of this thesis is to numerically estimate some conjectured arm exponents when there exist a number of open paths and closed dual paths that extend to the boundary of different sizes of boxes centering at the origin in bond invasion percolation on a plane square lattice by Monte-Carlo simulations. The results turn out to be supportive of the conjectured value in some case. The numerical estimate for the acceptance profile of invasion percolation at the critical point is also obtained, which suggests a neighborhood in which the liminf and limsup of the acceptance profile might fall. An efficient algorithm to simulate invasion percolation and to find disjoint paths on most regular 2-dimensional lattices are discussed.
dc.description.degree M.S.
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/62823
dc.language.iso en_US
dc.publisher Georgia Institute of Technology
dc.subject Percolation
dc.subject Critical percolation
dc.subject Invasion percolation
dc.subject Ford-Fulkerson algorithm
dc.subject Regression
dc.title Numerical estimates for arm exponents and the acceptance profile in two-dimensional invasion percolation
dc.type Text
dc.type.genre Thesis
dspace.entity.type Publication
local.contributor.advisor Damron, Michael
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isAdvisorOfPublication 4f8df015-77a8-4370-bcdd-aa6a4c4c516d
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
thesis.degree.level Masters
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
233.44 KB
Adobe Portable Document Format
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
3.86 KB
Plain Text