Related papers: Iterated Gilbert Mosaics and Poisson Tropical Plan…

We present a new approach to study measures on ensembles of contours, polymers or other objects interacting by some sort of exclusion condition. For concreteness we develop it here for the case of Peierls contours. Unlike existing methods,…

Let X be a plane in a torus over an algebraically closed field K, with tropicalization the matroidal fan Sigma. In this paper we present an algorithm which completely solves the question whether a given one-dimensional balanced polyhedral…

Tropical counting tools are useful for many enumerative questions. We count tropical multinodal surfaces using floor plans, looking at the case when two nodes are tropically close together, i.e., unseparated. We generalize tropical floor…

This is the second paper of a series dedicated to the study of Poisson structures of compact types (PMCTs). In this paper, we focus on regular PMCTs, exhibiting a rich transverse geometry. We show that their leaf spaces are integral affine…

Consider a random geometric graph $G$ with a vertex set defined by a Poisson point process with intensity $t>0$ in a convex body. We can generate a drawing of the graph by projecting the construction onto some plane $L$. Choosing different…

We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…

Let (E,D,P) be a flat vector bundle with a parabolic structure over a punctured Riemann surface, (M,g). We consider a deformation of the harmonic metric equation which we call the Poisson metric equation. This equation arises naturally as…

We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model.…

The compound decision problem for a vector of independent Poisson random variables with possibly different means has half a century old solution. However, it appears that the classical solution needs smoothing adjustment even when there are…

Coisotropic deformations of algebraic varieties are defined as those for which an ideal of the deformed variety is a Poisson ideal. It is shown that coisotropic deformations of sets of intersection points of plane quadrics, cubics and space…

Let X be a smooth algebraic variety over a field of characteristic 0. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O_X. These are stack-like versions of usual deformations. We prove that…

This paper is the third installment in a series of papers devoted to the computation of enumerative invariants of abelian surfaces through the tropical approach. We develop a pearl diagram algorithm similar to the floor diagram algorithm…

We introduce a procedure for constructing a generalized elliptic curve from a genus-one twisted curve, and we use this procedure to define an explicit, modular isomorphism between two compactifications of moduli stacks of elliptic curves…

This paper deals with the problem of model selection for a general class of integer-valued time series. We propose a penalized criterion based on the Poisson quasi-likelihood of the model. Under certain regularity conditions, the…

Tropical refined invariants of toric surfaces constitute a fascinating interpolation between real and complex enumerative geometries via tropical geometry. They were originally introduced by Block and G\"ottsche, and further extended by…

We study constrained percolation models on planar lattices including the $[m,4,n,4]$ lattice and the square tilings of the hyperbolic plane, satisfying certain local constraints on faces of degree 4, and investigate the existence of…

We consider planar quadrangulations with three marked vertices and discuss the geometry of triangles made of three geodesic paths joining them. We also study the geometry of minimal separating loops, i.e. paths of minimal length among all…

We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…

We consider the Alexander polynomial of a plane algebraic curve twisted by a linear representation. We show that it divides the product of the polynomials of the singularity links, for unitary representations. Moreover, their quotient is…

The dynamical system generated by the iterated calculation of the high order gaps between neighboring terms of a sequence of natural numbers is remarkable and only incidentally characterized at the boundary by the notable Proth-Glibreath…