In this paper, we observe the frog model, an infinite system of interacting random walks, on Z with an asymmetric underlying random walk. Under the assumption of transience with a fixed frog distribution, we construct an explicit formula for the moments of the lower bound of the model’s long-run range, as well as their asymptotic limits as the drift of the underlying random walk vanishes. We al...

Many prominent continuous-time stochastic volatility models exhibit certain functional relationships between price jumps and volatility jumps. We show that stochastic volatility models like the Ornstein-Uhlenbeck and other continous-time CARMA models as well as continous-time GARCH and EGARCH models all exhibit such functional relations. We investigate the asymptotic behaviour of certain functi...

We show that the set of Heisenberg polynomials furnishes a simple non-trivial example in the uniform treatment of Darboux’s method. MSC2010: 41A60; 33C15

Let C be a smooth projective curve in P1 × P1 of genus g 6= 4, and assume that it is birationally equivalent to a curve defined by a Laurent polynomial that is non-degenerate with respect to its Newton polygon ∆. Then we show that the convex hull ∆(1) of the interior lattice points of ∆ is a standard rectangle, up to a unimodular transformation. Our main auxiliary result, which we believe to be...

Schreyer has proved that the graded Betti numbers of a canonical tetragonal curve are determined by two integers b1 and b2, associated to the curve through a certain geometric construction. In this article we prove that in the case of a smooth projective tetragonal curve on a toric surface, these integers have easy interpretations in terms of the Newton polygon of its defining Laurent polynomia...

An algorithm is described that constructs, in a polynomial time, a Nash equilibrium in a finite game with additive aggregation and decreasing best responses. MSC2010 Classifications: 91A10; 91A04.

A complete description of dynamics in a neighborhood of a finite bunch of homoclinic loops to a saddle equilibrium state of a Hamiltonian system is given. MSC2010 numbers: 37J30, 37J40, 37D05, 37C29 DOI: 10.1134/S1560354714060069

In Dellunde et al. (J. Symbolic Logic 67(3) (2002) 997–1015), we determined the complete theory Te of modules of separably closed %elds of characteristic p and imperfection degree e, e∈! ∪ {∞}. Here, for 0 = e∈!, we describe the closed set of the Ziegler spectrum corresponding to Te. Further, we establish a correspondence between certain submodules and n-types and we investigate several notions...

A new research project has, quite recently, been launched to clarify how different, from systems in second order number theory extending ACA0, those in second order set theory extending NBG (as well as those in n+3-th order number theory extending the so-called Bernays Gödel expansion of full n+2-order number theory etc.) are. In this article, we establish the equivalence between ∆0-LFP and ∆ 1...

We study the graph structure of large random dissections of polygons sampled according to Boltzmann weights, which encompasses the case of uniform dissections or uniform p-angulations. As their number of vertices n goes to infinity, we show that these random graphs, rescaled by n−1/2, converge in the Gromov–Hausdorff sense towards a multiple of Aldous’ Brownian tree when the weights decrease su...