Rigorous results in Spin Glasses and Monomer-Dimer systems

In this work I reported recent results in the field of Statistical Mechanics of Equilibrium, and in particular in Spin Glass models and Monomer Dimer models . We start giving the mathematical background and the general formalism for Spin (Disordered) Models with some of their applications to physical and mathematical problems. Next we move on general aspects of the theory of spin glasses, in particular to the Sherrington-Kirkpatrick model which is of fundamental interest for the work. In Chapter 3, we introduce the Multi-species Sherrington-Kirkpatrick model (MSK), we prove the existence of the thermodynamical limit and the Guerra's Bound for the quenched pressure together with a detailed analysis of the annealed and the replica symmetric regime. The result is a multidimensional generalization of the Parisi's theory. Finally we brie y illustrate the strategy of the Panchenko's proof of the lower bound. In Chapter 4 we discuss the Aizenmann-Contucci and the Ghirlanda-Guerra identities for a wide class of Spin Glass models. As an example of application, we discuss the role of these identities in the proof of the lower bound. In Chapter 5 we introduce the basic mathematical formalism of Monomer Dimer models. We introduce a Gaussian representation of the partition function that will be fundamental in the rest of the work. In Chapter 6, we introduce an interacting Monomer-Dimer model. Its exact solution is derived and a detailed study of its analytical properties and related physical quantities is performed. In Chapter 7, we introduce a quenched randomness in the Monomer Dimer model and show that, under suitable conditions the pressure is a self averaging quantity. The main result is that, if we consider randomness only in the monomer activity, the model is exactly solvable.

Linking rural tourism to agriculture. Evidences from comparative case studies in Kosovo, Italy and Spain

Rural tourism has been widely promoted in the European Union as an effective measure counteracting economic and social challenges facing rural areas especially those with declining agriculture economies. Particularly its role is seen in provision and maintenance of public goods which are more and more demanded by the public and considered in the policymaking. In Kosovo, rural tourism has been developed through the support of the international organizations and private sector initiatives, with primary aim to generate additional income for rural households and sustainable management of natural and cultural resources. Anyhow, it could be stated that the use of territorial capital to enhance the quality of the tourist offer and undertake promotion at wider circles of people has not been well explored so far, particularly possible links with agriculture that would satisfy visitors demand. In this regard this research study analyzes involvement of local stakeholders and use of territorial capital to develop tourist offer in rural areas of Kosovo. Beside, study applies comparative approach with other two areas of the European Union, Appennino Bolognese in Italy and Alpujara in Spain, to understand and compare the process of rural tourism development and demand characteristics between Kosovo and these areas. A survey has been conducted in all three study areas with rural tourism visitors to understand their preferences for public and private goods and services when visiting rural areas and the role of agriculture in sustaining rural tourism. Results show that there is a potential to link rural tourism with agriculture in Kosovo, which would help in sustaining agriculture and add additional value to local food products, which in return would enhance the tourist offer and make it more attractive for the visitors but also for the farmers as an additional revenue generating sector.