Related papers: Non-standard boundary behaviour in two-component m…
We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…
In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…
Suppose that the edges of a complete graph are assigned weights independently at random and we ask for the weight of the minimal-weight spanning tree, or perfect matching, or Hamiltonian cycle. For these and several other common…
Concentration inequalities are fundamental tools in probabilistic combinatorics and theoretical computer science for proving that random functions are near their means. Of particular importance is the case where f(X) is a function of…
This paper studies the joint limiting behavior of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model, where the asymptotic regime is such that the dimension and sample size grow…
In this paper we revisited the classical problem of max-sum equivalence of randomly weighted sums in two dimensions. In opposite to the most papers in literature, we consider that there exists some interdependence between the primary random…
We study the Tracy-Widom (TW) distribution $f_\beta(a)$ in the limit of large Dyson index $\beta \to +\infty$. This distribution describes the fluctuations of the rescaled largest eigenvalue $a_1$ of the Gaussian (alias Hermite) ensemble…
We investigate the biased quenched trap model on top of a two-dimensional lattice in the case of diverging expected dwell times. By utilizing the double-subordination approach and calculating the return probability in $2$d, we explicitly…
This paper reviews the most common situations where one or more regularity conditions which underlie classical likelihood-based parametric inference fail. We identify three main classes of problems: boundary problems, indeterminate…
This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to…
Let $X(t), t\in \mathcal{T}$ be a centered Gaussian random field with variance function $\sigma^2(\cdot)$ that attains its maximum at the unique point $t_0\in \mathcal{T}$, and let $M(\mathcal{T}):=\sup_{t\in \mathcal{T}} X(t)$. For…
We investigate the role of the boundary in the symmetric simple exclusion process with competing nonlocal and local hopping events. With open boundaries, the system undergoes a first order phase transition from a finite density phase to an…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
We show under weak hypotheses that $\partial X$, the Roller boundary of a finite dimensional CAT(0) cube complex $X$ is the Furstenberg-Poisson boundary of a sufficiently nice random walk on an acting group $\Gamma$. In particular, we show…
Modeling of longitudinal data often requires diffusion models that incorporate overall time-dependent, nonlinear dynamics of multiple components and provide sufficient flexibility for subject-specific modeling. This complexity challenges…
We consider the nonlinear boundary value problem consisting of the equation \tag{1} -u" = f(u) + h, \quad \text{a.e. on $(-1,1)$,} where $h \in L^1(-1,1)$, together with the multi-point, Dirichlet-type boundary conditions \tag{2} u(\pm 1) =…
Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and…
Let $\mu$ be a probability measure on $\text{Out}(F_N)$ with finite first logarithmic moment with respect to the word metric, finite entropy, and whose support generates a nonelementary subgroup of $\text{Out}(F_N)$. We show that almost…
In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak…
The large-matrix limit laws of the rescaled largest eigenvalue of the orthogonal, unitary, and symplectic $n$-dimensional Gaussian ensembles -- and of the corresponding Laguerre ensembles (Wishart distributions) for various regimes of the…