4 papers
Square-Difference-Free Sets beyond the Three-Quarter Barrier
Dmitry Krachun
Let denote the largest cardinality of a subset of containing no nonzero square difference. While a construction certifying is alm…
Rotational invariance in critical planar lattice models
Hugo Duminil-Copin, Karol Kajetan Kozlowski, Dmitry Krachun +2
We prove that the large-scale properties of a number of two-dimensional lattice models are rotationally invariant. More precisely, we prove that the random-cluster model on the squ…
Critical exponents for planar random-cluster model with cluster-weight
Hong-Bin Chen, Hugo Duminil-Copin, Tiancheng He +4
Using the Baxter-Kelland-Wu coupling and the convergence of the height function of the six-vertex model to the Gaussian Free Field, we extract critical exponents for the planar cri…
Provable Quantization with Randomized Hadamard Transform
Ying Feng, Piotr Indyk, Michael Kapralov +2
Vector quantization via random projection followed by scalar quantization is a fundamental primitive in machine learning, with applications ranging from similarity search to federa…