PPT-First passage percolation on rotationally invariant fields

Allan Sly Princeton University September 2016 Joint work with Riddhipratim Basu Stanford and Vladas Sidoravicius NYU Shanghai First Passage Percolation Model an IID random field of numbers. In addition magnetic fields create a force only on moving charges The direction the magnetic field produced by a moving charge is perpendicular to the direction of motion The direction of the force due to a magnetic field is perpendicular to the dir s father was a wealthy Virginia plante Washington fought in the French and Indian War Washington fought in the French and Indian War led disorganized poor ly funded Continental army in led disorganized poor ly funded Continental army in the Revoluti 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 15. 14. A Chessboard Problem. ?. A . Bishop . can only move along a diagonal. Can a . bishop . move from its current position to the question mark?. Violating Measurement Independence without fine-tuning, conspiracy, or constraints on free will. Tim Palmer. Clarendon Laboratory. University of Oxford. T. o explain the experimental violation of Bell Inequalities, a putative theory of quantum physics must violate one (or more) of:. and calculus of shapes. © Alexander & Michael Bronstein, 2006-2010. tosca.cs.technion.ac.il/book. VIPS Advanced School on. Numerical Geometry of Non-Rigid Shapes . University of Verona, April 2010. the. . transverse. gauge links in . soft. . collinear. . effective. . theory. . Ignazio. . Scimemi. Universidad Complutense de Madrid (UCM). In . collaboration. . with. A. . Idilbi. , M. García Echevarría . Rahul Sharma and Alex Aiken (Stanford University). 1. Randomized Search. x. = . i. ;. y = j;. while . y!=0 . do. . x = x-1;. . y = y-1;. if( . i. ==j ). assert x==0. No!. Yes!.  . 2. Invariants. Rainscaping:. Soils 101. . Soils 101. Living, breathing dynamic system. Chemical, . physical . and biological characteristics. Soil . Formation -- 5 . Influencing Factors. C. limate . -. weathering, freeze, thaw, wetting, drying. Simulating percolation models. Guillermo . Amaral. Caesar. . Systems. - Argentina. Guillermo Amaral. 2. Guillermo Amaral. 3. Guillermo Amaral. 4. A virtual lab. Guillermo Amaral. 5. Percolation deals with…. COMPUTER Surface MICHAEL Massachusetts Massachusetts Received Th rotational Human the partial rotationally of set investigation one-dimensional o In performance variations p. for o Dmitri Krioukov. CAIDA/UCSD. M. . . Á. . Serrano, M. . Bogu. ñá. . UNT, March 2011. Percolation. Percolation is one of the most fundamental and best-studied critical phenomena in nature. In networks: the critical parameter is often average degree . Rahul Sharma and Alex Aiken (Stanford University). 1. Randomized Search. x. = . i. ;. y = j;. while . y!=0 . do. . x = x-1;. . y = y-1;. if( . i. ==j ). assert x==0. No!. Yes!.  . 2. Invariants. Zallen. ]. R. . Zallen. , . The Physics of Amorphous Solids. , Wiley-VCH, 2004.. This figure, from page 137 of . Zallen. , describes the problem in a 2D square mesh.. At some . precise. critical number of random snips, current flow stops.. Northeastern University, Boston. May 2012. Chennai Network Optimization Workshop. Percolation Processes. 1. Outline. Branching processes. Idealized model of epidemic spread. Percolation theory. Epidemic spread in an infinite graph.