wmin2eat optimal bounds Yitong Yin Nanjing University Joint work with: Alistair Sinclair (UC Berkeley) Piyush Srivastava(UC Berkeley) Daniel Stefankovic (Rochester)
Spatial Mixing and the Connective Constant: optimal bounds Yitong Yin Nanjing University Joint work with: Alistair Sinclair (UC Berkeley) Piyush Srivastava (UC Berkeley) Daniel Štefankovič (Rochester)
undirected graph G=(V,E) mtelinofdpof matchings amstnormindpetf matching
undirected graph G = (V,E) approximately counting # of of G matchings {independent sets} almost uniformly sampling a of G matching {independent set}
undirected graph G=(V,E) approximaely countingofof matchings ① computationally equivalent mnifomyamineof matching
undirected graph G = (V,E) approximately counting # of of G matchings {independent sets} almost uniformly sampling a of G matching {independent set} computationally equivalent
undirected graph G=(V,E) monomer-dimer model:set of all matchings M(G) partition function ZA(G)=XIMI M∈M(G)
Z(G) = X M2M(G) |M| monomer-dimer model: M(G) undirected graph G = (V,E) set of all matchings partition function
undirected graph G=(V,E) monomer-dimer model:set of all matchings M(G) partition function Z(G)=∑XM M∈M(G) λXMI Gibbs distribution (M)= ZG
Z(G) = X M2M(G) |M| monomer-dimer model: M(G) undirected graph G = (V,E) set of all matchings partition function µ(M) = |M| Z(G) Gibbs distribution