Search results for "HuR"

Statistical analysis of financial returns for a multiagent order book model of asset trading

2007

We recently introduced a realistic order book model [T. Preis, Europhys. Lett. 75, 510 (2006)] which is able to generate the stylized facts of financial markets. We analyze this model in detail, explain the consequences of the use of different groups of traders, and focus on the foundation of a nontrivial Hurst exponent based on the introduction of a market trend. Our order book model supports the theoretical argument that a nontrivial Hurst exponent implies not necessarily long-term correlations. A coupling of the order placement depth to the market trend can produce fat tails, which can be described by a truncated Lévy distribution.

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MR 2944715 Reviewed Zhu S. On the recursion formula for double Hurwitz numbers. Proceedings of the American Mathematical Society (2012) 140, no. 11, …

2013

Let $\mu = (\mu_{1}, \mu_{2}, \ldots, \mu_{m})$ and $\nu = (\nu_{1}, \nu_{2}, \ldots, \nu_{n})$ be two partitions of a positive integer $d$. In this paper, the author considers degree $d$ branched coverings of $\mathbb{P}^{1}$ with at most two special points, $0$ and $\infty$. Specifically, the purpose of the author is to give a recursion formula for double Hurwitz numbers $H^{g}_{\mu, \nu}$ by the cut-join analysis. Here, $H^{g}_{\mu, \nu}$ denotes the number of genus $g$ branched covers of $\mathbb{P}^{1}$ with branching date corresponding to $\mu$ and $\nu$ over $0$ and $\infty$, respectively. Furthemore, as application, the author gets a polynomial identity for linear Goulden-Jackson-Va…

MR 2827979 Reviewed Lando, S. K. Hurwitz numbers: on the edge between combinatorics and geometry. Proceedings of the International Congress of Mathem…

2012

Object of study in this paper are the Hurwitz numbers. They were introduced by Hurwitz in the end of nineteenth century and still they are of great interest. The Hurwitz numbers are important in topology because they enumerate ramified coverings of two-dimensional surfaces, but not only. The author observes that their importance in modern research is mainly due to their connections with the geometry of the moduli space of curves. Moreover, they are of interest in mathematical physics and group theory. The purpose of this paper is to describe the progress made in the last couple of decades in understanding Hurwitz numbers.

Irreducibility of Hurwitz spaces of coverings with monodromy groups Weyl groups of type W(B_d)

2007

Let Y be a smooth, connected, projective complex curve of genus ≥0. R. Biggers and M. Fried [J. Reine Angew. Math. 335, 87–121 (1982; Zbl 0484.14002), Trans. Am. Math. Soc. 295, No. 1, 59–70 (1986; Zbl 0601.14022)] proved the irreducibility of the Hurwitz spaces which parametrize coverings of ℙ 1 whose monodromy group is a Weyl of type W(D d ). Here we prove the irreducibility of Hurwitz spaces that parametrize coverings of Y with monodromy group a Weyl group of type W(B d ).

Hurwitz spaces of Galois coverings of P^1, whose Galois groups are Weyl groups

2006

We prove the irreducibility of the Hurwitz spaces which parametrize Galois coverings of P^1 whose Galois group is an arbitrary Weyl group and the local monodromies are reflections. This generalizes a classical theorem due to Clebsch and Hurwitz.

On coverings with special points and monodromy group a Weyl group of type B_d

2014

In this paper we study Hurwitz spaces parameterizing coverings with special points and with monodromy group a Weyl group of type Bd. We prove that such spaces are irreducible if k > 3d ? 3. Here, k denotes the number of local monodromies that are reflections relative to long roots.

On the irreducibility of Hurwitz spaces of coverings with an arbitrary number of special points

2013

In this paper we study Hurwitz spaces of coverings of Y with an arbitrary number of special points and with monodromy group a Weyl group of type D_d, where Y is a smooth, complex projective curve. We give conditions for which these spaces are irreducible.

MR 2918162 Reviewed Van der Geer G. and Kouvidakis A. The Hodge bundle on Hurwitz spaces. Pure and Applied Mathematics Quarterly (2011) 7, no. 4, 129…

2012

In this paper the authors consider the Hurwitz space $H_{g, \, d}$ that parametrizes degree $d$ simple coverings of $\mathbb{P}^{1}$ with $b = 2 g - 2 + 2d$ branch points. The compactification $\bar{H}_{g, \, d}$ of this Hurwitz space is the space of admissible covers of genus $g$ and degree $d$, $f: C \rightarrow P$, where $C$ is a nodal curve and $P$ is a stable $b$-pointed curve of genus $0$. Assigning to $f: C \rightarrow P$ the stabilized model of $C$, one defines a natural map $\phi: \bar{H}_{g, \, d} \rightarrow \bar{M}_{g}$ where $\bar{M}_{g}$ denotes the moduli space of stable curves of genus $g$. The Hurwitz space $\bar{H}_{g, \, d}$ carries a natural $\mathbb{Q}$-divisor class, t…

Modelling rainfall interarrival times and rainfall depths at daily scale

2023

Analysis of daily rainfall data, and subsequent modelling of some derived variables concerning rainfall, is fundamental in different areas such as agricultural, ecological, and engineering disciplines. A way of studying the alternance of consecutive rainy days (wet spells) and no-rainy days (dry spells) is through the interarrival time (IT), which is the time elapsed between two consecutives rainy days. If we suppose that IT observations are independent and identically distributed (i.i.d.), ITs are usually modelled through a renewal processes. The simplest renewal process is the Bernoulli process with ITs geometrically distributed. The need to suppose a non-constant probability of rain brin…