309 papers
This paper establishes a unified canonical framework linking the Maximal Entropy Simple Symmetric Exclusion Process to both Unitary Dyson Brownian Motion and Free Unitary Brownian Motion by leveraging Schur polynomials and symmetric group characters to derive explicit spectral decompositions and hydrodynamic limits that reveal entropic forces and nonlinear transport equations.
This paper generalizes a previous result on outlier eigenvectors by establishing that for sparse non-Hermitian random matrices with finite-rank perturbations, the squared projection of an outlier eigenvector onto the spike eigenspace converges in probability to $1-|\mu|^{-2}$, thereby solving Open Problem 5.
This paper establishes optimal strong and weak convergence rates for slow-fast systems driven by multiplicative -stable Lévy noises by overcoming challenges in exponential ergodicity and gradient estimates through coupling and spatial periodic methods, while also deriving explicit formulas for tangent maps induced by nonlinear immersions.
This paper proves that the empirical spectral distribution of the normalized Laplacian for linear preferential attachment graphs in the Barabási-Albert regime converges weakly in probability to a deterministic measure on [0, 2], which is characterized by the expected diagonal Green function of the associated Pólya-point graph using a combination of resolvent methods, random-walk representations, and concentration inequalities.
This paper establishes the well-posedness of reflected stochastic partial differential equations in infinite-dimensional domains under a fully local monotone framework, utilizing a key variational inequality to generalize results for various important models including stochastic Allen-Cahn, p-Laplacian, Cahn-Hilliard, and 3D tamed Navier-Stokes equations.
This paper establishes sharp estimates for functions harmonic with respect to -dependent rectilinear stable processes in balls under radial exterior data, utilizing the construction of global barrier functions for the associated -dependent rectilinear fractional Laplacian.
This paper introduces a general category-theoretic framework for epistemic uncertainty that unifies various imprecise probability theories, models their interrelationships, and demonstrates how both Bayesian updating and possibilistic conditioning emerge as specific instances of a generalized belief updating process based on change of enrichment.
This paper establishes a strengthened comparison theorem for the extreme eigenvalues of sums of independent random symmetric matrices against Gaussian counterparts, leveraging this result to improve eigenvalue bounds across various fields and providing the first complete proof of the injectivity properties for sparse random dimension reduction maps conjectured by Nelson & Nguyen.
This paper generalizes Backhausz and Szegedy's result on the infinite regular tree by proving that the Gaussian wave is the unique typical process with Green's function covariance for any infinite tree of finite cone type satisfying mild expansion, thereby establishing the convergence of local eigenvector distributions to the Gaussian wave for random bipartite biregular graphs and generic configuration models.