Saba Lepsveridze

activity

20232026

collaborators

8 papers

cs.DS2026

Color Coding for the Sherrington-Kirkpatrick Model

Alina Harbuzova, Saba Lepsveridze, Mahbod Majid +1

We give a polynomial-time algorithm for approximating the partition function of mean-field mixed $p$ -spin models to arbitrarily high accuracy throughout the second-moment regime. T…

math.CO2026

Graphs with connectivity $3/4 - ε$ are globally synchronizing

Saba Lepsveridze, Sam Zhang

We study synchronization in the Kuramoto model on finite graphs. We prove that there is an absolute constant $η > 0$ such that every finite simple graph $G$ on $n$ vertices with mini…

math.ST2026

Optimal Spectral Algorithms for Correlated Two-view Models in High Dimensions

Hang Du, Henry Hu, Saba Lepsveridze

We study high-dimensional inference in correlated two-view models, focusing on spectral methods for strong detection and weak recovery. We introduce a general framework, motivated…

math.CO2026

Uniform Geodesic Drawings of Graphs

Saba Lepsveridze, Oriol Solé-Pi

We study crossing numbers of dense graph drawings whose vertices are uniformly distributed either on the unit sphere or in a compact convex planar domain. We prove a sharp inequali…

math.PR2026

Sharp Threshold for the Convergence of Nonstationary Averaging

Saba Lepsveridze, Elchanan Mossel

We study non-stationary averaging processes, where each term of a sequence is a weighted average of previous terms, namely $a_{n + 1} = \sum_{j = 1}^{n} p_{n} (j) a_{j}$ . Our results extend c…

math.PR2025

Optimal Thresholds for Monotone Non-Boolean Functions

Saba Lepsveridze, Allen Lin

Let $[q] = {0, 1, \dots, q - 1}$ , let $Δ [q]$ denote the simplex of probability measures on $[q]$ , and let $γ$ denote the Lebesgue measure normalized on $Δ [q]$ . We prove that for any…

math.CO2023

Uniacute Spherical Codes

Saba Lepsveridze, Aleksandre Saatashvili, Yufei Zhao

A spherical $L$ -code, where $L \subseteq [- 1, \infty)$ , consists of unit vectors in $R^{d}$ whose pairwise inner products are contained in $L$ . Determining the maximum cardin…

math.CO2023

Size of the largest sum-free subset of $[n]^{3}$ and $[n]^{4}$

Saba Lepsveridze, Yihang Sun

We determine the density of the largest sum-free subset of the lattice cube ${1, 2, \dots, n}^{d}$ for $d = 3$ and $d = 4$ . This solves a conjecture of Cameron and Aydinian in dime…