| dc.contributor |
Ortega Cerdà, Joaquim |
|
| dc.creator |
Arraz Almirall, Alexis |
|
| dc.date |
2018-10-08T07:59:53Z |
|
| dc.date |
2018-10-08T07:59:53Z |
|
| dc.date |
2018-06-27 |
|
| dc.date.accessioned |
2024-12-16T10:26:48Z |
|
| dc.date.available |
2024-12-16T10:26:48Z |
|
| dc.identifier |
http://hdl.handle.net/2445/125123 |
|
| dc.identifier.uri |
http://fima-docencia.ub.edu:8080/xmlui/handle/123456789/21543 |
|
| dc.description |
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Joaquim Ortega Cerdà |
|
| dc.description |
[en] In this project we deal with random analytic functions. Here we specifically use Gaussian analytic functions. Without technicalities, a GAF $f$ (for short) is a random holomorphic function on a region of $\mathbb{C}$ such that $( f ( z 1 ) , ..., f ( z n ))$ is a random vector with normal distribution. One way to generate them is using linear combinations of holomorphic functions whose coefficients are Gaussian random variables in $\mathbb{C}$ (or in $\mathbb{R}$ in special cases). For finding the zero set of a GAF we work on four isometric - invariant Hilbert spaces of analytic functions: the Fock space in $\mathbb{C}$, the finite space of polynomials in $\mathbb{S}^2$, the weighted Bergman space in $\mathbb{D}$ and the Paley - Wiener space. The first intensity determines the average of the distribution of the zero set of a GAF, and the Edelman - Kostlan formula gives an explicit expression of it. A result of uniqueness, called Calabi’s Rigidity, concludes that the first intensity determines the distribution of the zero set of a GAF. At the end, some examples made in C++ and gnuplot clarify the theory in these Hilbert spaces. |
|
| dc.format |
81 p. |
|
| dc.format |
application/pdf |
|
| dc.language |
eng |
|
| dc.rights |
cc-by-nc-nd (c) Alexis Arraz Almirall, 2018 |
|
| dc.rights |
http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
|
| dc.rights |
info:eu-repo/semantics/openAccess |
|
| dc.source |
Treballs Finals de Grau (TFG) - Matemàtiques |
|
| dc.subject |
Funcions de variables complexes |
|
| dc.subject |
Teoria geomètrica de funcions |
|
| dc.subject |
Processos puntuals |
|
| dc.subject |
Treballs de fi de grau |
|
| dc.subject |
Functions of complex variables |
|
| dc.subject |
Geometric function theory |
|
| dc.subject |
Point processes |
|
| dc.subject |
Bachelor's theses |
|
| dc.title |
Zeros of random analytic functions |
|
| dc.type |
info:eu-repo/semantics/bachelorThesis |
|