arXiv subjects

Barış Yeşiloğlu

Publications and source records attributed to Barış Yeşiloğlu.

3 recordsLinked to original sources

arXiv2025

Analysis of Clustering and Degree Index in Random Graphs and Complex Networks

The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the corresponding theoretical analysis in a random graph setup turns out to be tractable. On the other hand, the clustering index, based on a similar reasoning, is first introduced in this manuscript. Computing exact expressions for the expected clustering index turns out to be more challenging even in the case of Erdős-Rényi graphs, and our results are on obtaining relevant upper bounds. These are also complemented with observations based on Monte Carlo simulations. Besides the Erdős-Rényi case, we also do simulation-based analysis for random regular graphs, the Barabási-Albert model and the Watts-Strogatz model.

math.PR↗

arXiv2024

Scattering for Stochastic Nonlinear Schrödinger Equations with additive noise

We study the scattering for the energy-subcritical stochastic nonlinear Schrödinger equation (SNLS) with additive noise. In particular, we examine the long-time behavior of solutions associated with the noise $ϕ(x)g(t,ω)dB(t,ω)$ formed by a Schwartz function $ϕ$, and an adapted process $g(t,ω)$ satisfying certain decay. Essentially, the aim of the current paper is to prove almost sure scattering in the spaces $L^2$ and the pseudo-conformal space $Σ$ for an initial data in $Σ$; also in $H^1$ for an initial data in $H^1$.

math.AP↗

arXiv2023

Global Well-posedness for The Fourth-order Nonlinear Schrödinger Equations on $\mathbb{R}^{2}$

We study the global well-posedness of the two-dimensional defocusing fourth-order Schrödinger initial value problem with power type nonlinearities $\vert u\vert^{2k}u$ where $k$ is a positive integer. By using the $I$-method, we prove that global well-posedness is satisfied in the Sobolev spaces $H^{s}(\mathbb{R}^{2})$ for $2-\frac{3}{4k}<s<2$.

math.AP↗