6 citations · 13 across the 12 of their papers we have counts for
18 papers
Dragon curves in Littlewood roots
Marcus Michelen, Oren Yakir
A Littlewood polynomial is a polynomial whose coefficients lie in . While the majority of roots of a Littlewood polynomial of large degree are near the unit circle, nu…
Gaussian limits of lattice Higgs models with complete symmetry breaking
Frederick Rajasekaran, Oren Yakir, Yanxin Zhou
Given any compact connected matrix Lie group and any lattice dimension , we construct a massive Gaussian scaling limit for the -valued lattice Yang-Mills-Higgs theor…
Optimal factor matchings for point processes on non-amenable unimodular graphs
Yinon Spinka, Oren Yakir
Consider a unit-intensity point process on the vertex set of a transitive non-amenable unimodular graph. We study invariant matchings between and having small typic…
A simple proof of local universality for roots of Kac polynomials
Marcus Michelen, Oren Yakir
Let be a random polynomial of degree with i.i.d. mean-zero and finite variance random coefficients. It is well known that the roots of cluster uniformly around the…
Correlation decay for U(1) lattice Higgs theory: the case of small mass
Sourav Chatterjee, Oren Yakir
We study the lattice Yang-Mills-Higgs model with inverse gauge coupling and Higgs length , in the ``complete breakdown of symmetry" regime. For lattice dimension $d\ge 2…
Optimal matchings of randomly perturbed lattices
Dor Elboim, Yinon Spinka, Oren Yakir
Consider a point process in Euclidean space obtained by perturbing the integer lattice with independent and identically distributed random vectors. Under mild assumptions on the la…
Law of large numbers for the discriminant of random polynomials
Marcus Michelen, Oren Yakir
Let be a random polynomial of degree , whose coefficients are independent and identically distributed random variables with mean-zero and variance one. Let denote…
Limit law for root separation in random polynomials
Marcus Michelen, Oren Yakir
Let be a random polynomial of degree whose coefficients are independent and identically distributed random variables. We study the separation distances between roots…
Large charge fluctuations in the hierarchical Coulomb gas
Alon Nishry, Oren Yakir
The two-dimensional one-component plasma (OCP) is a model of electrically charged particles which are embedded in a uniform background of the opposite charge, and interact through…
Fluctuations in the logarithmic energy for zeros of random polynomials on the sphere
Marcus Michelen, Oren Yakir
Smale's Seventh Problem asks for an efficient algorithm to generate a configuration of points on the sphere that nearly minimizes the logarithmic energy. As a candidate startin…
The random Weierstrass zeta function II. Fluctuations of the electric flux through rectifiable curves
Mikhail Sodin, Aron Wennman, Oren Yakir
Consider a random planar point process whose law is invariant under planar isometries. We think of the process as a random distribution of point charges and consider the electric f…
The random Weierstrass zeta function I. Existence, uniqueness, fluctuations
Mikhail Sodin, Aron Wennman, Oren Yakir
We describe a construction of random meromorphic functions with prescribed simple poles with unit residues at a given stationary point process. We characterize those stationary pro…
Universality of Poisson limits for moduli of roots of Kac polynomials
Nicholas A. Cook, Hoi H. Nguyen, Oren Yakir +1
We give a new proof of a recent resolution by Michelen and Sahasrabudhe of a conjecture of Shepp and Vanderbei that the moduli of roots of Gaussian Kac polynomials of degree , c…
Approximately half of the roots of a random Littlewood polynomial are inside the disk
Oren Yakir
We prove that for large , all but polynomials of the form have roots inside the unit disk. This solves a problem from Ha…
Fluctuations of linear statistics for Gaussian perturbations of the lattice
Oren Yakir
We study the point process in obtained by adding an independent Gaussian vector to each point in . Our main concern is the asymptotic size of fluct…
The minimum modulus of Gaussian trigonometric polynomials
Oren Yakir, Ofer Zeitouni
We prove that the minimum of the modulus of a random trigonometric polynomial with Gaussian coefficients, properly normalized, has limiting exponential distribution.
Recovering the lattice from its random perturbations
Oren Yakir
Given a -dimensional Euclidean lattice we consider the random set obtained by adding an independent Gaussian vector to each of the lattice points. In this note we provide a simp…
Boundary Effects in the Discrete Bass Model
Gadi Fibich, Tomer Levin, Oren Yakir
To study the effect of boundaries on diffusion of new products, we introduce two novel analytic tools: The indifference principle, which enables us to explicitly compute the aggreg…