D. Krachun

activity

20162026

most citedRotational invariance in critical planar lattice models

10 citations · 13 across the 14 of their papers we have counts for

collaborators

16 papers

math.PR2026

Supercritical sharpness for the random cluster representation of real-valued spin models

Trishen S. Gunaratnam, Dmitry Krachun, Christoforos Panagiotis +2

We study the supercritical regime $β > β_{c}$ of a large family of real-valued spin models on $Z^{d}$ , including the Blume-Capel and $P (φ)$ models. We consider their random clust…

math.CO2026

Square-Difference-Free Sets beyond the Three-Quarter Barrier

Dmitry Krachun

Let $D (N)$ denote the largest cardinality of a subset of ${1, \dots, N}$ containing no nonzero square difference. While a construction certifying $D (N) \geq (1 - o (1)) N^{1/2}$ is alm…

math.PR2026

Critical exponents for planar random-cluster model with cluster-weight $q = 4$

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…

cs.LG2026

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…

math.CO2024

Discrete Brunn-Minkowski Inequality for subsets of the cube

Lars Becker, Paata Ivanisvili, Dmitry Krachun +1

We show that for all $A, B \subseteq {0, 1, 2}^{d}$ we have $∣ A + B ∣ \geq (∣ A ∣∣ B ∣)^{l o g (5) / (2 l o g (3))} .$ We also show that for all finite $A, B \subset Z^{d}$ , and any $V…

math.CO2023

Tight lower bound on $∣ A + λ A ∣$ for algebraic integer $λ$

D. Krachun, F. Petrov

We prove an asymptotically tight lower bound on $∣ A + λ A ∣$ for $A \subset C$ and algebraic integer $λ$ . The proof combines strong version of Freiman's theorem, structural the…