We introduce a transfer matrix formalism for the (annealed) Ising model coupled to two-dimensional causal dynamical triangulations. Using the Krein-Rutman theory of positivity preserving operators we study several properties of the emerging transfer matrix. In particular, we determine regions in the quadrant of parameters β, µ > 0 where the infinite-volume free energy converges, yielding results on the convergence and asymptotic properties of the partition function and the Gibbs measure.2000 MSC. 60F05, 60J60, 60J80.

In this work we study the annealed Potts model coupled to two dimensional causal triangulations with periodic boundary condition. Using duality on a torus, we provide a relation between the free energy of the Potts model coupled CTs and its dual. This duality relation follows from the FK representation for the Potts model. In order to determine a region where the critical curve for the model can be located we use the duality relation and the high-temperature expansion. This is done by outlining a region where the infinite-volume Gibbs measure exists and is unique and a region where the finite-volume Gibbs measure has no weak limit (in fact, does not exist if the volume is large enough). We also provide lower and upper bounds for the infinitevolume free energy.2000 MSC. 60F05, 60J60, 60J80.

Abstract. In this paper, we derive the large deviation principle for the Potts model on the complete bipartite graph Kn,n as n increases to infinity. Next, for the Potts model on Kn,n, we provide an extension of the method of aggregate path coupling that was originally developed in [20] for the mean-field Blume-Capel model and in [21] for a general mean-field setting that included the Generalized Curie-Weiss-Potts model analyzed in [19]. We use the aggregate path coupling method to identify and determine the threshold value βs separating the rapid and slow mixing regimes for the Glauber dynamics of the Potts model on Kn,n.

El presente trabajo estima una descomposición factorial dinámica para la inflación peruana, usando datos desagregados mensuales del índice de precios al consumidor de Lima Metropolitana de Enero de 2000 hasta Diciembre de 2019. Uno de los objetivos de la macroeconomía es explicar las fuentes agregadas de cambios en los precios de los bienes de una economía. Este modelo permite identificar precios relativos idiosincráticos, precios relativos agregados y precios absolutos, que representan los choques de oferta y demanda que pueden aparecer en una economía. La componente común a todos los rubros del IPC sirve como una medida alternativa de la inflación subyacente, y nuestros resultados muestran que esta componente está altamente correlacionada con la inflación subyacente publicada por el BCRP. En general, los resultados obtenidos en el presente trabajo son robustos para diferentes estructuras de dependencia intertemporal para los factores considerados.