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Fastest mixing Markov chain on a graph
Markov chains second largest eigenvalue modulus fast mixing semidefinite programming subgradient method
2015/8/11
We consider a symmetric random walk on a connected graph, where each edge is labeled with the probability of transition between the two adjacent vertices. The associated Markov chain has a uniform equ...
There exists no distance-regular graph with intersection array {56,36,9;1,3,48}
distance-regular graph intersection array
2010/11/23
We prove that a distance-regular graph with intersection array {56,36,9;1,3,48} does not exist. This intersection array is from the table of feasible parameters for distance-regular graphs in "Distanc...
A group has a planar Cayley complex if and only if it has a VAP-free Cayley graph
planar Cayley complex VAP-free Cayley graph
2010/11/23
We prove that a group has a planar Cayley complex if and only if it has a Cayley graph that can be embedded in the euclidean plane without accumulation points of vertices.
Let $C^*(E)$ be the graph $C^*$-algebra associated to a graph E and let J be a gauge invariant ideal in $C^*(E)$. We compute the cyclic six-term exact sequence in $K$-theory of the associated extensio...
The q-Gelfand-Tsetlin graph, Gibbs measures and q-Toeplitz matrices
The q-Gelfand-Tsetlin graph Gibbs measures
2010/11/12
The problem of the description of finite factor representations of the infinite-dimensional unitary group, investigated by Voiculescu in 1976, is equivalent to the description of all totally positive...
Splice Diagram Singularities and The Universal Abelian Cover of Graph Orbifolds
Splice Diagram Singularities The Universal Abelian Cover of Graph Orbifolds
2010/11/9
Given a rational homology sphere M, whose splice diagram satisfy the semigroup condition, Neumann and Wahl were able to define a complete intersection surface singularity called splice diagram singul...
We consider the {\it infinite Johnson graph} $J_{\infty}$ whose vertex set consists of all subsets $X\subset {\mathbb N}$ satisfying $|X|=|{\mathbb N}\setminus X|=\infty$ and whose edges are pairs of...
The threshold-two contact process on a random r-regular graph has a first order phase transition
The threshold-two contact process r-regular graph phase transition
2010/11/12
We consider the discrete time threshold-two contact process on a random $r$-regular graph on $n$ vertices. In this process, a vertex with at least two occupied neighbors at time $t$ will be occupied ...
M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra
Formality Deformation Quantization Operads
2010/12/1
We show that the zeroth cohomology of Kontsevich’s graph complex is isomorphic to the Grothendieck-Teichm¨uller Lie algebra grt. The map is explicitly described.