Related papers: Local limit theorem for directed polymers beyond t…

In this paper, we study the local boundedness of local weak solutions to the following parabolic equation associated with fractional $p$-Laplacian type operators $$ \partial_t…

We consider ILPs, where each variable corresponds to an integral point within a polytope $\mathcal{P}$, i. e., ILPs of the form $\min\{c^{\top}x\mid \sum_{p\in\mathcal P\cap \mathbb Z^d} x_p p = b, x\in\mathbb Z^{|\mathcal P\cap \mathbb…

We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…

We consider a one--particle bound quantum mechanical system governed by a Schr\"odinger operator $\mathscr{H} = -\Delta + v\,f(r)$, where $f(r)$ is an attractive central potential, and $v>0$ is a coupling parameter. If $\phi \in…

We discuss $L^p(\mathbb R^n)$ boundedness for Fourier multiplier operators that satisfy the hypotheses of the H\"ormander multiplier theorem in terms of an optimal condition that relates the distance $|\frac 1p-\frac12|$ to the smoothness…

We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite $p$th power energy in a (not necessarily complete) metric measure space equipped with a globally doubling measure supporting a global…

We consider a directed polymer interacting with a diluted pinning potential restricted to a line. We characterize explicitely the set of disorder configurations that give rise to localization of the polymer. We study both relevant cases of…

Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for…

The study of two-dimensional Coulomb gases lies at the interface of statistical physics and non-Hermitian random matrix theory. In this paper we give a large deviation principle (LDP) for the empirical fields obtained, under the canonical…

We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and introduce a class of invariants that refine the classical…

The exact solution of directed self-avoiding walks confined to a slit of finite width and interacting with the walls of the slit via an attractive potential has been calculated recently. The walks can be considered to model the…

If a bounded domain can be covered by the polydisk through a rational proper holomorphic map, then the Bergman projection is $L^p$-bounded for $p$ in a certain range depending on the ramified rational covering. This result can be applied to…

The well-known fact following from the Holmgren-John-Tataru uniqueness theorem is a local approximate boundary $L_2$-controllability of the dynamical system governed by the wave equation. Generalizing this result, we establish the…

We consider the model of a directed polymer in a random environment defined on the infinite cluster of supercritical Bernoulli bond percolation in dimensions $d \geq 3$. For this model, it was proved in arXiv:2205.06206 that for almost…

We investigate $L^p$ boundedness of the maximal function defined by the averaging operator $f\to \mathcal{A}_t^s f$ over the two-parameter family of tori $\mathbb{T}_t^{s}:=\{ ( (t+s\cos\theta)\cos\phi,\,(t+s\cos\theta)\sin\phi,\,…

We study the local asymptotic behavior of divergence-like functionals of a family of $d$-dimensional Infinitely Divisible Random Fields. Specifically, we derive limit theorems of surface integrals over Lipschitz manifolds for this class of…

We study a model of two polymers confined to a slit with sticky walls. More precisely, we find and analyse the exact solution of two directed friendly walks in such a geometry on the square lattice. We compare the infinite slit limit, in…

Optimization methods that make use of derivatives of the objective function up to order $p > 2$ are called tensor methods. Among them, ones that minimize a regularized $p$th-order Taylor expansion at each step have been shown to possess…

We consider a directed polymer model in dimension $1+1$, where the disorder is given by the occupation field of a Poisson system of independent random walks on $\mathbb Z$. In a suitable continuum and weak disorder limit, we show that the…

Let $W_N(\beta) = \mathrm{E}_0\left[e^{ \sum_{n=1}^N \beta \omega(n,S_n) - N\beta^2/2}\right]$ be the partition function of a two-dimensional directed polymer in a random environment, where $\omega(i,x), i\in \mathbb{N}, x\in \mathbb{Z}^2$…