Related papers: KPZ in a multidimensional random geometry of multi…
We consider the Bergman space on the complex plane. We prove an analogue of Schwarz's reflection principle for unbounded quasidisks.
Multidimensional factorization method is formulated in arbitrary curvilinear coordinates. Particular cases of polar and spherical coordinates are considered and matrix potentials with separating variables are constructed. A new class of…
In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts that increase coverage are accepted. The process continues indefinitely on an infinite substrate, and we analyze the…
Explicit formulae for the B\'ezier coefficients of the constrained dual Bernstein basis polynomials are derived in terms of the Hahn orthogonal polynomials. Using difference properties of the latter polynomials, efficient recursive scheme…
Multiple zeta values (MZVs) with certain repeated arguments or certain sums of cyclically generated MZVs are evaluated as rational multiple of powers of $\pi^2$. In this paper, we give a short and simple proof of the remarkable evaluations…
We study extensions and generalizations of the Schmidt Subspace Theorem in various settings. In particular, we prove results for algebraic points of bounded degree, giving a sharp version of Schmidt's theorem for quadratic points in the…
We give the formulation in extended superspace of an $N=2$ supersymmetric KP hierarchy using chirality preserving pseudo-differential operators. We obtain two quadratic hamiltonian structures, which lead to different reductions of the KP…
We show that noncommutative differential forms on $k[x]$, $k$ a field, are of the form $\Omega^1=k_\lambda[x]$ where $k_\lambda\supset k$ is a field extension. We compute the case $C\supset R$ explicitly, where $\Omega^1$ is 2-dimensional.…
We show that the $i$-dimensional plaqutte random-cluster model with coefficients in $\mathbb{Z}_q$ is dual to a $(d-i)$-dimensional plaquette random cluster model. In addition, we explore boundary conditions, infinite volume limits, and…
We apply a number of schemes which variationally improve perturbation theory for the Kardar-Parisi-Zhang equation in order to extract estimates for the dynamic exponent z. The results for the various schemes show the same broad features,…
We present a complete proof of the exact formula for the one-point distribution for the narrow-wedge Hopf-Cole solution to the Kardar-Parisi-Zhang (KPZ) equation. This presentation is intended to be self-contained so no previous knowledge…
We work towards a question raised by Cluckers and Glazer in [CG25], to bring the dimension growth upper bounds and lower bounds for the worst case closer together. To this end, we introduce a sublinear sharpened version of the projective…
In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…
We investigate the probability that a random quadratic form in ${\mathbb{Z}}[x_1,...,x_n]$ has a totally isotropic subspace of a given dimension. We show that this global probability is a product of local probabilities. Our main result…
In this paper, we provide a probabilistic interpretation of the Volkenborn integral; this allows us to extend results by T. Kim et al about sums of Euler numbers to sums of Bernoulli numbers. We also obtain a probabilistic representation of…
Fekete, Jord\'an and Kaszanitzky [4] characterised the graphs which can be realised as 2-dimensional, infinitesimally rigid, bar-joint frameworks in which two given vertices are coincident. We formulate a conjecture which would extend their…
We estimate whether there is an embedding from one n-dimensional rectangle into another which expands every k-dimensional area. Our estimate is sharp up to a constant factor in each dimension.
We use the properties of Hermite and Kamp\'e de F\'eriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of…
We establish isomorphism ranges for the comparison maps between algebraic and topological K-groups, extending classical Quillen-Lichtenbaum conjecture to separated complex schemes of finite type after refinement. Additionally, we…
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…