相关论文: On Random Multiple Dirichlet Series

We consider Dirichlet problems for fully nonlinear mixed local-nonlocal non-translation invariant operators. For a bounded $C^2$ domain $\Omega \subset \mathbb{R}^d,$ let $u\in C(\mathbb{R}^d)$ be a viscosity solution of such Dirichlet…

Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the…

Random boundary conditions are one of the simplest realizations of quenched disorder. They have been used as an illustration of various conceptual issues in the theory of disordered spin systems. Here we review some of these results.

The paper examines one-dimensional total variation flow equation with Dirichlet boundary conditions. Thanks to a new concept of "almost classical" solutions we are able to determine evolution of facets -- flat regions of solutions. A key…

We develop the Perron-Wiener-Brelot method of solving the Dirichlet problem at the Martin boundary of a fine domain in $\RR^n$ ($n\ge2$).

Using the direct method of the calculus of variations we investigate the existence, uniqueness and continuous dependence on parameters for solutions of second order discrete anisotropic equations with Dirichlet boundary conditions.

Let P_{n,d,D} denote the graph taken uniformly at random from the set of all labelled planar graphs on {1,2,...,n} with minimum degree at least d(n) and maximum degree at most D(n). We use counting arguments to investigate the probability…

We give an explicit formula for the Hilbert Series of an algebra defined by a linearly presented, standard graded, residual intersection of a grade three Gorenstein ideal.

We consider the zero distribution of random polynomials of the form $P_n(z) = \sum_{k=0}^n a_k B_k(z)$, where $\{a_k\}_{k=0}^{\infty}$ are non-trivial i.i.d. complex random variables with mean $0$ and finite variance. Polynomials…

In this short note, we consider the elliptic problem $$ \lambda \phi + \Delta \phi = \eta|\phi|^\sigma \phi,\quad \phi\big|_{\partial \Omega}=0,\quad \lambda, \eta \in \mathbb{C}, $$ on a smooth domain $\Omega\subset \mathbb{R}^N$, $N\ge…

The lacunary series are the most classical examples among all the power series whose circle of convergence constitutes a natural boundary (\cite[\S~93-94, p.~372-383]{Di}, \cite[\S 7.43, p.~223]{Ti}, ...). In this Note, we study a family of…

We consider the inverse boundary value problem of determining the Lam\'e moduli of an isotropic, static elasticity equations of system at the boundary from the localized Dirichlet-to-Neumann map. Assuming appropriate local regularity…

The random walk in Dirichlet environment is a random walk in random environment where the transition probabilities are independent Dirichlet random variables. This random walk exhibits a property of statistical invariance by time-reversal…

We consider random Schr\"odinger operators with Dirichlet boundary conditions outside lattice approximations of a smooth Euclidean domain and study the behavior of its lowest-lying eigenvalues in the limit when the lattice spacing tends to…

In this paper, we give a mathematically rigorous proof of the averaging behavior of oscillatory surface integrals. Based on ergodic theory, we find a sharp geometric condition which we call irrational direction dense condition, abbreviated…

We present an overview of bounds on zeros of $L$-functions and obtain some improvements under weak conjectures related to the Goldbach problem.

We show that for a uniformly irreducible random walk on a graph, with bounded range, there is a Floyd function for which the random walk converges to its corresponding Floyd boundary. Moreover if we add the assumptions, $p^{(n)}(v,w)\leq C…

Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimensional case, the notion of reach takes its place. In this…

We consider the Dirichlet boundary value problem for graphical maximal submanifolds inside Lorentzian type ambient spaces, and obtain general existence and uniqueness results which apply to any codimension.

We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.