Distribution of roots of Eulerian polynomials

Key Points

• The roots of Eulerian polynomials converge to a specific log-Cauchy distribution, enhancing understanding of their distribution.
• Empirical measures show that asymptotic moments remain constant, indicating a strong relationship with Nörlund's numbers.
• The study illustrates the convergence behavior of polynomial roots and their significance in mathematical analysis.
• These findings may have implications for further research on polynomial roots and their associated distributions.