---
res:
  bibo_abstract:
  - "This thesis deals with the study of stochastic processes and their ergodicity
    properties. The\r\nvariety of problems encountered calls for a set of different
    approaches, ranging from classical to\r\nmodern ones: a special place is held
    by probabilistic methods based on couplings, by functional\r\ninequalities, and
    by the theory of gradient flows in the space of measures.\r\n\r\nThe material
    is organized as follows. Chapter 1 contains the introduction to this thesis, starting\r\nwith
    a general presentation of some of the relevant topics. Section 1.1 is dedicated
    to the\r\ntheory of gradient flows in metric spaces, and introduces the first
    contribution of this thesis\r\n[DSMP24], which is presented in detail in Chapter
    2. Section 1.2 moves to the topic of\r\ncurvature of Markov chains, concluding
    with a brief description of our second contribution\r\n[Ped23], which is included
    in Chapter 3. Section 1.3 discusses applications of stochastic\r\nprocesses to
    the theory of sampling, in particular the recent framework of score-based diffusion\r\nmodels,
    and our contribution [PMM24], which is contained in Chapter 4. Section 1.4 discusses\r\nsome
    related problems, concerning the regularization properties of the heat flow. It
    serves\r\nas a motivation for the work [BP24], which we report in Chapter 5. Finally,
    Section 1.5\r\ndiscusses the last contribution of this thesis, which can be found
    in Chapter 6. It deals with\r\nthe convergence to equilibrium of a particular
    stochastic model from quantitative genetics:\r\nthis is established via some functional
    inequalities, which we prove with probabilistic arguments\r\nbased on couplings.\r\n@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Francesco
      foaf_name: Pedrotti, Francesco
      foaf_surname: Pedrotti
      foaf_workInfoHomepage: http://www.librecat.org/personId=d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
  bibo_doi: 10.15479/at:ista:17336
  dct_date: 2024^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2663-337X
  dct_language: eng
  dct_publisher: Institute of Science and Technology Austria@
  dct_title: Functional inequalities and convergence of stochastic processes@
...