Related papers: Stochastic Fixed Points and Nonlinear Perron-Frobe…

For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that…

A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In this work we explore this in (finite-dimensional) stochastic…

We prove that conservation of probability for the free heat semigroup on a Riemannian manifold $M$ (namely stochastic completeness), hence a linear property, is equivalent to uniqueness of positive, bounded solutions to nonlinear evolution…

This paper combines the decomposition technique ($\sigma$-stability) in random functional analysis with the deterministic theory of asymptotically pointwise contractions to provide a complete self-contained derivation of a fixed point…

In this survey we review some recent rigorous results on large N problems in quantum field theory, stochastic quantization and singular stochastic PDEs, and their mean field limit problems. In particular we discuss the O(N) linear sigma…

In this paper we prove existence of nonnegative bounded solutions for the non-autonomous prescribed mean curvature problem in non-parametric form on an open bounded domain $\Omega$ of $\mathbb{R}^N$. The mean curvature, that depends on the…

We prove an equivariant version of the classical Menger-Nobeling theorem regarding topological embeddings: Whenever a group $G$ acts on a finite-dimensional compact metric space $X$, a generic continuous equivariant function from $X$ into…

We prove the $\Gamma$-convergence of sequences of differentially constrained, random integral functionals of the form \begin{equation*} \int_{U} f\Big(\omega, x/\varepsilon, \mathbb{A} u\Big) \mathrm{d} x \end{equation*} for the class of…

Suppose that $G=(V, E)$ be a locally finite and connected graph with symmetric weight and uniformly positive measure, where $V$ denotes the vertex set and $E$ denotes the edge set. We are concered with the following problem $$…

Given $\epsilon \in (0,1)$, a probability measure $\mu$ on $\Omega\subset\mathbb{R}^p$ and a semi-algebraic set $K\subset X\times\Omega$, we consider the feasible set $X^*_\epsilon=\{x\in X:{\rm Prob}[(x,\omega)\in K]\geq 1-\epsilon\}$…

We obtain central limit theorem, local limit theorems and renewal theorems for stationary processes generated by skew product maps $T(\om,x)=(\te\om,T_\om x)$ together with a $T$-invariant measure, whose base map $\te$ satisfies certain…

Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…

We prove a couple of results on local continuous extension of proper holomorphic maps $F:D \rightarrow \Omega$, $D, \Omega \varsubsetneq \mathbb{C}^n$, making local assumptions on $\partial{D}$ and $\partial{\Omega}$. The first result…

In this paper, we study the solvability problem for one kind of fully coupled forward-backward stochastic difference equations (FBS{\Delta}Es). With the help of the necessary and sufficient condition for the solvability of the linear…

It is proved a theorem providing necessary and sufficient conditions enabling one to map a nonlinear system of first order partial differential equations, polynomial in the derivatives, to an equivalent autonomous first order system…

We propose an explicit construction of the solution of a stationary stochastic recursion of the form $X\circ\theta=\phi(X)$ on a semi-ordered Polish space, when the monotonicity of $\phi$ is not assumed. This solution exists on an enriched…

We observe stationary random tessellations $X=\{\Xi_n\}_{n\ge1}$ in $\mathbb{R}^d$ through a convex sampling window $W$ that expands unboundedly and we determine the total $(k-1)$-volume of those $(k-1)$-dimensional manifold processes which…

We define a random model for the moments of the new eigenfunctions of a point scat-terer on a 2-dimensional rectangular flat torus. In the deterministic setting,Seba conjectured these moments to be asymptotically Gaussian, in the…

Unitary ensembles of large N x N random matrices with a non-Gaussian probability distribution P[H] ~ exp{-TrV[H]} are studied using a theory of polynomials orthogonal with respect to exponential weights. Asymptotically exact expressions for…

Let phi be a Dubins-Freedman random homeomorphism on [0,1] derived from the base measure uniform on the vertical line x=1/2, and let f be a periodic function satisfying that |f(x)-f(0)| = o(1/log log log 1/x). Then the Fourier expansion of…