Konrad Anand
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View article: Approximate Counting for Spin Systems in Sub-Quadratic Time
Approximate Counting for Spin Systems in Sub-Quadratic Time Open
We present two randomised approximate counting algorithms with $\widetilde{O}(n^{2-c}/\varepsilon^2)$ running time for some constant $c>0$ and accuracy $\varepsilon$: (1) for the hard-core model with fugacity $\lambda$ on graphs with ma…
View article: Sink-Free Orientations: A Local Sampler with Applications
Sink-Free Orientations: A Local Sampler with Applications Open
For sink-free orientations in graphs of minimum degree at least 3, we show that there is a deterministic approximate counting algorithm that runs in time O((n^33/ε^32)log(n/ε)), a near-linear time sampling algorithm, and a randomised appro…
View article: Rapid mixing of the flip chain over non-crossing spanning trees
Rapid mixing of the flip chain over non-crossing spanning trees Open
We show that the flip chain for non-crossing spanning trees of $n+1$ points in convex position mixes in time $O(n^8\log n)$. We use connections between Fuss-Catalan structures to construct a comparison argument with a chain similar to Wils…
View article: Perfect sampling of $q$-spin systems on $\mathbb{Z}^{2}$ via weak spatial mixing
Perfect sampling of $q$-spin systems on $\mathbb{Z}^{2}$ via weak spatial mixing Open
We present a perfect marginal sampler of the unique Gibbs measure of a spin system on \mathbb{Z}^{2} . The algorithm is an adaptation of a previous “lazy depth-first” approach by the authors, but relaxes the requirement of strong spatial m…
View article: Approximate Counting for Spin Systems in Sub-Quadratic Time
Approximate Counting for Spin Systems in Sub-Quadratic Time Open
We present two randomised approximate counting algorithms with $\widetilde{O}(n^{2-c}/\varepsilon^2)$ running time for some constant $c>0$ and accuracy $\varepsilon$: (1) for the hard-core model with fugacity $λ$ on graphs with maximum deg…
View article: Perfect Sampling for Hard Spheres from Strong Spatial Mixing
Perfect Sampling for Hard Spheres from Strong Spatial Mixing Open
We provide a perfect sampling algorithm for the hard-sphere model on subsets of $\mathbb{R}^d$ with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate samplin…
View article: Perfect Sampling of $q$-Spin Systems on $\mathbb Z^2$ via Weak Spatial Mixing
Perfect Sampling of $q$-Spin Systems on $\mathbb Z^2$ via Weak Spatial Mixing Open
We present a perfect marginal sampler of the unique Gibbs measure of a spin system on $\mathbb Z^2$. The algorithm is an adaptation of a previous `lazy depth-first' approach by the authors, but relaxes the requirement of strong spatial mix…
View article: Perfect Sampling in Infinite Spin Systems via Strong Spatial Mixing
Perfect Sampling in Infinite Spin Systems via Strong Spatial Mixing Open
We present a simple algorithm that perfectly samples configurations from the unique Gibbs measure of a spin system on a potentially infinite graph $G$. The sampling algorithm assumes strong spatial mixing together with subexponential growt…
View article: Probabilistic Analysis of RRT Trees
Probabilistic Analysis of RRT Trees Open
This thesis presents analysis of the properties and run-time of the Rapidly-exploring Random Tree (RRT) algorithm. It is shown that the time for the RRT with stepsize $ε$ to grow close to every point in the $d$-dimensional unit cube is $Θ\…