Related papers: A Dynamical Analogue of Sen's Theorem
We fill a gap in the proof of one of the central theorems in Epp's paper, concerning $p$-cyclic extensions of complete discrete valuation rings.
We study in this paper logarithmic derivatives associated to derivations on graded complete Lie algebra, as well as the existence of inverses. These logarithmic derivatives, when invertible, generalize the exp-log correspondence between a…
In network science, collective dynamics of complex systems are typically modelled as (nonlinear, often including many-body) vertex-level update rules evolving over a graph interaction structure. In recent years, frameworks that explicitly…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
Let $p$ be a prime number, $\Bbbk$ a field of characteristic $p$ and $G$ a finite $p$-group acting on a standard graded polynomial ring $S = \Bbbk[x_1, \ldots, x_n]$ as degree-preserving $\Bbbk$-algebra automorphisms. Assume that $G$ is…
In this paper, we write down the local Brauer classes of the endomorphism algebras of motives attached to non-CM primitive Hecke eigenforms for all supercuspidal primes in terms of traces of adjoint lifts at auxiliary primes. We give an…
We introduce two tools, dynamical thickening and flow selectors, to overcome the infamous discontinuity of the gradient flow endpoint map near non-degenerate critical points. More precisely, we interpret the stable fibrations of certain…
We exhibit infinite lists of ramification indices $\delta$ for which the classical Lie groups over the ring of integers of $p$-adic fields admit a faithful self-similar action on a regular rooted $\delta$-ary tree in such a way that the…
We examine the behavior of the coefficients of powers of polynomials over a finite field of prime order. Extending the work of Allouche-Berthe, 1997, we study a(n), the number of occurring strings of length n among coefficients of any power…
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…
We study the spreading dynamics on graphs with a power law degree distribution p_k ~ k^-gamma with 2<gamma<3, as an example of a branching process with diverging reproductive number. We provide evidence that the divergence of the second…
A discrete group which admits a faithful, finite dimensional, linear representation over a field $\mathbb F$ of characteristic zero is called linear. This note combines the natural structure of semi-direct products with work of A. Lubotzky…
We propose a relation the expansions of regular and irregular semiclassical conformal blocks at different branch points making use of the connection between the accessory parameters of the BPZ decoupling equations to the logarithm…
The algebraic properties of formal power series, whose coefficients show factorial growth and admit a certain well-behaved asymptotic expansion, are discussed. It is shown that these series form a subring of $\mathbb{R}[[x]]$. This subring…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
We design exact polynomial expansions of a class of Feynman--Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related combinatorial quantities. The accuracy of the expansions at any…
We study the long-time behaviour of the growth-fragmentation equation, a nonlocal linear evolution equation describing a wide range of phenomena in structured population dynamics. We show the existence of a spectral gap under conditions…
We present an axiomatic framework for the residue structures induced by Prufer extensions with a stress upon the intimate connection between their arithmetic and arboreal theoretic properties. The main result of the paper provides an…
Patterns and forms adopted by Nature, such as the shape of living cells, the geometry of shells and the branched structure of plants, are often the result of simple dynamical paradigms. Here we show that a growing self-interacting string…
Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on…