Related papers: The motion of a random string
This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…
Ambiguities of the so-called Thiemann regularization in Loop Quantum Cosmology lead to freedom in how to construct a particular quantization prescription. So far three distinct examples of such have been proposed in the literature. For two…
We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other things generalised Hirota form, exact evaluation of the…
We consider the evolution of a network of strings in an expanding universe, allowing for the formation of junctions between strings of different tensions. By explicitly including, in the velocity-dependent evolution equations for the…
Evolution occurs in populations of reproducing individuals. It is well known that population structure can affect evolutionary dynamics. Traditionally, natural selection is studied between mutants that differ in reproductive rate, but are…
We investigate the selective forces that promote the emergence of modularity in nature. We demonstrate the spontaneous emergence of modularity in a population of individuals that evolve in a changing environment. We show that the level of…
The Bernoulli convolution with parameter $\lambda\in(0,1)$ is the measure on $\bf R$ that is the distribution of the random power series $\sum\pm\lambda^n$, where $\pm$ are independent fair coin-tosses. This paper surveys recent progress on…
While generic competitive systems exhibit mixtures of hierarchy and cycles, real-world systems are predominantly hierarchical. We demonstrate and extend a mechanism for hierarchy; systems with similar agents approach perfect hierarchy in…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory as well as number theory and…
We define a natural extension of pluriclosed flow aiming at constructing solutions of the Hull-Strominger system. We give several geometric formulations of this flow, which yield a series of a priori estimates for the flow and also for the…
In this paper we consider symplectic and Hamiltonian structures of systems generated by actions of sigma-model type and show that these systems are naturally connected with specific symplectic geometry on loop spaces of Riemannian and…
We show that the Lagrangian of classical mechanics on a Riemannian manifold of bounded geometry carries a periodic solution of motion with rescribed energy, provided the potential satisfies an asymptotic growth condition, changes sign, and…
The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate…
The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…
We study the regularity properties of random wavelet series constructed by multiplying the coefficients of a deterministic wavelet series with unbounded I.I.D. random variables. In particular, we show that, at the opposite to what happens…
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
We construct natural Riemannian metrics on Seiberg-Witten moduli spaces and study their geometry.
We elucidate physical aspects of path signatures by formulating randomised path developments within the framework of matrix models in quantum field theory. Using tools from physics, we introduce a new family of randomised path developments…
In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the…
We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in $\mathbb{R}^d$. We prove convergence of the convex hull in the space of all convex and compact subsets of $\mathbb{R}^d$, equipped…