7 citations · 19 across the 24 of their papers we have counts for
24 papers
Numerical simulations of the spread from the mean of the SLE and Multiple SLE dynamics
Phillip Kim, Vlad Margarint
The Schramm-Loewner Evolution (SLE) describes a family of fractal curves that arise in the study of the scaling limits of many planar Statistical Physics models. These curves are m…
Neural Networks and Schramm-Loewner Evolutions
Neilesh Shrotri, Vlad Margarint
In this manuscript, we explore the application of neural networks to predict the natural parameter of Schramm-Loewner Evolution (SLE) theory. SLE is a family of r…
Splitting algorithm and normed convergence for drawing the random Loewner curves
Jiaming Chen, Vlad Margarint
Recent advances in Schramm-Loewner evolution have driven increasing interest in non-standard Loewner flows. In this work, we propose a novel splitting algorithm to simulate random…
On the analytic extension of Random Riemann Zeta Functions for some probabilistic models of the primes
Vlad Margarint, Stanislav Molchanov
The first step in the formulation and study of the Riemann Hypothesis is the analytic continuation of the Riemann Zeta Function (RZF) in the full Complex Plane with a pole at …
On the cover time of Brownian motion on the Brownian continuum random tree
George Andriopoulos, David A. Croydon, Vlad Margarint +1
Upon almost-every realisation of the Brownian continuum random tree (CRT), it is possible to define a canonical diffusion process or `Brownian motion'. The main result of this arti…
Scaling Limits of Disorder Relevant Non-Binary Spin Systems
Liuyan Li, Vlad Margarint, Rongfeng Sun
In [7], Caravenna, Sun and Zygouras gave general criteria for the partition functions of binary valued spin systems with a relevant random field perturbation to have non-trivial co…
Local Central Limit Theorem for unbounded long-range potentials
Eric O. Endo, Roberto Fernández, Vlad Margarint +1
We prove the equivalence between the integral central limit theorem and the local central limit theorem for two-body potentials with long-range interactions on the lattice $\mathbb…
A Gaussian free field approach to the natural parametrisation of SLE
Vlad Margarint, Lukas Schoug
We construct the natural parametrisation of SLE using the Gaussian free field, complementing the corresponding results for SLE for by Benoist and for $κ\in (4,…
Rate of Convergence in Multiple SLE using Random Matrix Theory
Andrew Campbell, Kyle Luh, Vlad Margarint
We provide an order of convergence for a version of the Carathéodory convergence for the multiple SLE model with a Dyson Brownian motion driver towards its hydrodynamic limit, for…
A deterministic approach to Loewner-energy minimizers
Tim Mesikepp
We study two minimization questions: the nature of curves which minimize the Loewner energy among all curves from 0 to a fixed , and the n…
Local Central Limit Theorem for Long-Range Two-Body Potentials at Sufficiently High Temperatures
Eric O. Endo, Vlad Margarint
Dobrushin and Tirozzi [14] showed that, for a Gibbs measure with the finite-range potential, the Local Central Limit Theorem is implied by the Integral Central Limit Theorem. Campa…
Perturbations of Multiple Schramm-Loewner Evolution with Two Non-colliding Dyson Brownian Motions
Jiaming Chen, Vlad Margarint
In this article, we study multiple , for , driven by Dyson Brownian motion. This model was introduced in the unit disk by Cardy in connection with the Calogero-Su…
Law of the SLE tip
Oleg Butkovsky, Vlad Margarint, Yizheng Yuan
We analyze the law of the SLE tip at a fixed time in capacity parametrization. We describe it as the stationary law of a suitable diffusion process, and show that it has a density…
Splitting algorithm and normed convergence for drawing the random fractal Loewner curves
Jiaming Chen, Vlad Margarint
In the first part of the paper we propose and study the approximation of the trace via the Ninomiya-Victoir splitting algorithm. We prove the uniform convergence in probabi…
On Loewner chains driven by semimartingales and complex Bessel-type SDEs
Vlad Margarint, Atul Shekhar, Yizheng Yuan
We prove existence (and simpleness) of the trace for both forward and backward Loewner chains under fairly general conditions on semimartingale drivers. As an application, we show…
Quasi-Sure Stochastic Analysis through Aggregation and SLE Theory
Vlad Margarint
We study SLE theory with elements of Quasi-Sure Stochastic Analysis through Aggregation. Specifically, we show how the latter can be used to construct the SLE traces quasi-…
Continuity of Zero-Hitting Times of Bessel Processes and Welding Homeomorphisms of SLE
Dmitry Beliaev, Atul Shekhar, Vlad Margarint
We consider a family of Bessel Processes that depend on the starting point and dimension , but are driven by the same Brownian motion. Our main result is that almost surely…
Continuity in in theory using a constructive method and Rough Path Theory
Dmitry Beliaev, Terry J. Lyons, Vlad Margarint
Questions regarding the continuity in of the traces and maps appear very naturally in the study of SLE. In order to study the first question, we consider a natural coup…
A new approach to SLE phase transition
Dmitry Beliaev, Terry J. Lyons, Vlad Margarint
It is well know that curves exhibit a phase transition at . For they are simple curves with probability one, for they are not. The standard proof is bas…
Complex Solutions to Bessel SDEs and SLEs
Atul Shekhar, Vlad Margarint
We consider a variant of Bessel SDE by allowing the solution to be complex valued. Such SDEs appear naturally while studying the trace of Schramm-Loewner-Evolutions (SLE). We estab…
An asymptotic radius of convergence for the Loewner equation and simulation of traces via splitting
James Foster, Terry Lyons, Vlad Margarint
In this paper, we shall study the convergence of Taylor approximations for the backward Loewner differential equation (driven by Brownian motion) near the origin. More concretely,…
Convergence to closed-form distribution for the backward at some random times and the phase transition at
Terry J. Lyons, Vlad Margarint, Sina Nejad
We study a one-dimensional SDE that we obtain by performing a random time change of the backward Loewner dynamics in . The stationary measure for this SDE has a closed-…
Convergence in High Probability of the Quantum Diffusion in a Random Band Matrix Model
Vlad Margarint
We consider Hermitian random band matrices in dimensions. The matrix elements indexed by are independent, uniformly dist…
Proof of the Weak Local Law for Wigner Matrices using Resolvent Expansions
Vlad Margarint
The aim of this paper is to provide a novel proof for the Local Semicircle Law for the Wigner ensemble. The core of the proof is the intensive use of the algebraic structure that a…