Istruzione dibattimentale e poteri del giudice sulla prova

La previsione codicistica di un potere giudiziale sulla prova è stata costruita come limite al principio dispositivo secondo cui il verdetto sulla penale responsabilità dell’imputato può fondarsi essenzialmente su prove introdotte dalle parti. Nell’ottica di salvaguardare il carattere indisponibile dell’oggetto del processo, l’ordinamento ammette una ingerenza probatoria ope iudicis nella misura in cui si connoti in termini di eccezionalità e residualità, fungendo da semplice completamento di un’istruttoria di parte rimasta lacunosa

A polynomial upper bound for the mixing time of edge rotations on planar maps

We consider a natural local dynamic on the set of all rooted planar maps with $n$ edges that is in some sense analogous to "edge flip" Markov chains, which have been considered before on a variety of combinatorial structures (triangulations of the $n$-gon and quadrangulations of the sphere, among others). We provide the first polynomial upper bound for the mixing time of this "edge rotation" chain on planar maps: we show that the spectral gap of the edge rotation chain is bounded below by an appropriate constant times $n^{-11/2}$. In doing so, we provide a partially new proof of the fact that the same bound applies to the spectral gap of edge flips on quadrangulations, which makes it possible to generalise a recent result of the author and Stauffer to a chain that relates to edge rotations via Tutte's bijection

Growing uniform planar maps face by face

We provide “growth schemes” for inductively generating uniform random -angulations of the sphere with faces, as well as uniform random simple triangulations of the sphere with faces. In the case of -angulations, we provide a way to insert a new face at a random location in a uniform -angulation with faces in such a way that the new map is precisely a uniform -angulation with faces. Similarly, given a uniform simple triangulation of the sphere with faces, we describe a way to insert two new adjacent triangles so as to obtain a uniform simple triangulation of the sphere with faces. The latter is based on a new bijective presentation of simple triangulations that relies on a construction by Poulalhon and Schaeffer