arXiv subjects

Emilio De Santis

Publications and source records attributed to Emilio De Santis.

At least 19 recordsLinked to original sources

arXiv2026

Zero-temperature stochastic Ising model on one-dimensional quasi-transitive graphs

We consider the zero-temperature stochastic Ising process describing $\pm 1$ spin-flip dynamics on an infinite one-dimensional quasi-transitive graph $G=(V,E)$ with finite interaction range $K$. We prove that the zero-temperature limit of the Glauber dynamics for this Ising model exhibits a Type $\mathcal{I}$ behavior (infinite fluctuations of all vertices) if and only if the graph possesses the so-called \emph{shrink property}. For graphs lacking this property, we introduce an algorithmic framework based on an auxiliary spatial automaton to distinguish, in finite time, between Type $\mathcal{F}$ behavior (almost sure local fixation) and Type $\mathcal{M}$ behavior (a mixed regime characterized by the presence of blinkers). We prove that the classification among these three regimes is algorithmically decidable. Furthermore, we provide a constructive example of a graph supporting blinkers of arbitrarily large size.

math.PR↗

arXiv2026

Strategic Partitioning and Manipulability in Two-Round Elections

We consider a two-round election model involving $m$ voters and $n$ candidates. Each voter is endowed with a strict preference list ranking the candidates. In the first round, the candidates are partitioned into two subsets, $A$ and $B$, and voters select their preferred candidate from each. Provided there are no ties, the two respective winners advance to a second round, where voters choose between them according to their initial preference lists. We analyze this scenario using a probabilistic framework based on a spatial voting model with cyclically constructed preference lists and uniformly distributed ideal points. Our objective is to determine the optimal initial partition of $A$ and $B$ that maximizes a target candidate's probability of winning. We analytically evaluate this success probability and derive its asymptotic behavior as the number of candidates $n \to \infty$. A key finding is that the asymptotically optimal relative width of the main discrete cluster converges precisely to one-fifth of the total number of candidates. Finally, we provide computational results and confidence intervals derived from simulation algorithms that validate the analytical framework. Specifically, we demonstrate that the probability of the universal victory event rapidly approaches $1$ as the electorate size increases.

cs.GT↗

arXiv2026

Synaptic Classification via Spike-Triggered Extrapolation

This work introduces a statistical procedure to infer the interaction graph of neuronal networks modeled by Galves-L\"ocherbach dynamics. The methodology performs bivariate inference, identifying synaptic links from the spike trains of pairs of neurons without observing the rest of the network. We propose a Macro-Micro Extrapolation algorithm to address data sparsity by inferring interactions in the limit $\Delta \to 0^+$. The core component is a Spike-Triggered Estimator that leverages the local reset property to decouple synaptic jumps from background noise. By employing an adaptive logic that switches between sample averaging and Pyramid Extrapolation, the framework categorizes connections as excitatory, inhibitory, or null. Numerical simulations demonstrate that the classifier identifies synapses without error across varying noise regimes and complex network topologies, even for observation windows broader than those predicted by the current theoretical bounds.

q-bio.NC↗

arXiv2025

Voting Profiles Admitting All Candidates as Knockout Winners

A set of $2^n$ candidates is presented to a commission. At every round, each member of this commission votes by pairwise comparison, and one-half of the candidates is deleted from the tournament, the remaining ones proceeding to the next round until the $n$-th round (the final one) in which the final winner is declared. The candidates are arranged on a board in a given order, which is maintained among the remaining candidates at all rounds. A study of the size of the commission is carried out in order to obtain the desired result of any candidate being a possible winner. For $2^n$ candidates with $n \geq 3$, we identify a voting profile with $4n -3$ voters such that any candidate could win simply by choosing a proper initial order of the candidates. Moreover, in the setting of a random number of voters, we obtain the same results, with high probability, when the expected number of voters is large.

math.CO↗

arXiv2025

A new look at perfect simulation for chains with infinite memory

In this article we introduce two new perfect simulation algorithms for chains with infinite memory. Both algorithms belong to the coupling of past procedures. The novelty of our approach is that it allows to include unknown states to the possible past symbols such that we can also deal with sparsely distributed past dependencies. In our first algorithm, spontaneous occurrence of symbols is possible. This means that there is a positive probability that the chain chooses the next symbol independently of the past. Our second algorithm deals with the case in which spontaneous occurrence of symbols is not possible. Chains with infinite memory are discrete-time stochastic processes in which the distribution of the next symbol depends on all past symbols. These transition probabilities are described by a probability kernel. Our results give conditions on the way the dependency of the transition kernel on long past strings decays, guaranteeing that our algorithms stop after a finite number of steps almost surely. Strengthening these conditions, we show that the mean number of steps of our algorithms is finite. We discuss the consequence of having a coupling from the past algorithm with such properties and we present examples in which our results can be applied while others result in the literature cannot be applied.

math.PR↗

arXiv2023

Zero-temperature stochastic Ising model on planar quasi-transitive graphs

We study the zero-temperature stochastic Ising model on some connected planar quasi-transitive graphs, which are invariant under rotation and translation. The initial spin configuration is distributed according to a Bernoulli product measure with parameter $ p\in(0,1) $. In particular, we prove that if $ p=1/2 $ and the graph underlying the model satisfies the planar shrink property (which causes each finite cluster to shrink to a site and then vanish with positive probability) then all vertices flip infinitely often almost surely.

math.PR↗

arXiv2022

Existence and construction of voting situations concordant with ranking patterns

Referring to a standard context of voting theory, and to the classic notion of voting situation, here we show that it is possible to observe any arbitrary set of elections' outcomes, no matter how paradoxical it may appear. On this purpose we use results, presented in a recent paper of us, that hinge on the concept of ranking pattern concordant with a probability model for non-negative random variables and on a related role of special load-sharing models. Our results here will be obtained by suitably extending those therein, and by converting them into the context of voting.

math.PR↗

arXiv2021

Load-sharing dependence models and construction of voting situations for any arbitrary ranking schemes

In this paper we present a study about minima among random variables, about the context of voting theory, and about paradoxes related with such topics. In the field of reliability theory, the term load-sharing model is commonly used to designate a special type of multivariate survival models. We demonstrate the effectiveness that such dependence models can have also in some other fields, such as those of interest here. Several important, and by now classic, papers have been devoted to single out and to prove general conclusions in the field of voting theory. We reformulate and achieve such conclusions by developing a method of proof, alternative to the existing ones, and completely probabilistic in nature. As main features of this method, we focus attention on ranking schemes associated to m-tuples of non-negative random variables and suitably single out a special subclass of load-sharing models. Then we show that all possible ranking schemes can be conveniently obtained by only considering such a special family of survival models. This result leads to some new insight about the construction of voting situations which give rise to all possible types of voting paradoxes. Our method and related implications will be also illustrated by means of some examples and informative remarks.

math.PR↗

arXiv2021

Estimating the interaction graph of stochastic neuronal dynamics by observing only pairs of neurons

We address the questions of identifying pairs of interacting neurons from the observation of their spiking activity. The neuronal network is modeled by a system of interacting point processes with memory of variable length. The influence of a neuron on another can be either excitatory or inhibitory. To identify the existence and the nature of an interaction we propose an algorithm based only on the observation of joint activity of the two neurons in successive time slots. This reduces the amount of computation and storage required to run the algorithm, thereby making the algorithm suitable for the analysis of real neuronal data sets. We obtain computable upper bounds for the probabilities of false positive and false negative detection. As a corollary we prove the consistency of the identification algorithm.

math.ST↗

arXiv2020

Ranking graphs through Markov chains and hitting times

In the present paper we show that for any given digraph $\mathbb{G} =([n], \vec{E})$, i.e. an oriented graph without self-loops and 2-cycles, one can construct a 1-dependent Markov chain and $n$ identically distributed hitting times $T_1, \ldots , T_n $ on this chain such that the probability of the event $T_i > T_j $, for any $i, j = 1, \ldots n$, is larger than $\frac{1}{2}$ if and only if $(i,j)\in \vec{E}$. This result is related to various paradoxes in probability theory, concerning in particular non-transitive dice.

math.PR↗

arXiv2020

Stochastic precedence and minima among dependent variables

The notion of stochastic precedence between two random variables emerges as a relevant concept in several fields of applied probability. When one consider a vector of random variables $X_1,...,X_n$, this notion has a preeminent role in the analysis of minima of the type $\min_{j \in A} X_j$ for $A \subset \{1, \ldots n\}$. In such an analysis, however, several apparently controversial aspects can arise (among which phenomena of "non-transitivity"). Here we concentrate attention on vectors of non-negative random variables with absolutely continuous joint distributions, in which a case the set of the multivariate conditional hazard rate (m.c.h.r.) functions can be employed as a convenient method to describe different aspects of stochastic dependence. In terms of the m.c.h.r. functions, we first obtain convenient formulas for the probability distributions of the variables $\min_{j \in A} X_j$ and for the probability of events $\{X_i=\min_{j \in A} X_j\}$. Then we detail several aspects of the notion of stochastic precedence. On these bases, we explain some controversial behavior of such variables and give sufficient conditions under which paradoxical aspects can be excluded. On the purpose of stimulating active interest of readers, we present several comments and pertinent examples.

math.PR↗

arXiv2019

Constrained Monte Carlo Markov Chains on Graphs

This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov chain is constrained over an underlying graph, so that states are viewed as vertices and the transition between two states can have positive probability only in presence of an edge connecting them. The analysis is carried out on the basis of the relationship between the support of the target distribution and the connectedness of the graph.

math.PR↗

arXiv2019

Infinite paths on a random environment of $\mathbb{Z}^2$ with bounded and recurrent sums

This paper considers a random structure on the lattice $\mathbb{Z}^2$ of the following kind. To each edge $e$ a random variable $X_e$ is assigned, together with a random sign $Y_e \in \{-1,+1\}$. For an infinite self-avoiding path on $\mathbb{Z}^2$ starting at the origin consider the sequence of partial sums along the path. These are computed by summing the $X_e$'s for the edges $e$ crossed by the path, with a sign depending on the direction of the crossing. If the edge is crossed rightward or upward the sign is given by $Y_e$, otherwise by $-Y_e$. We assume that the sequence of $X_e$'s is i.i.d., drawn from an arbitrary common law and that the sequence of signs $Y_e$ is independent, with independent components drawn from a law which is allowed to change from horizontal to vertical edges. First we show that, with positive probability, there exists an infinite self-avoiding path starting from the origin with bounded partial sums. Moreover the process of partial sums either returns to zero or at least it returns to any neighborhood of zero infinitely often. These results are somewhat surprising at the light of the fact that, under rather mild conditions, there exists with probability $1$ two sites with all the paths joining them having the partial sums exceeding in absolute value any prescribed constant.

math.PR↗

arXiv2018

G-games with coalitions

This paper models games where the strategies are nodes of a graph G (we denote them as G-games) and in presence of coalition structures. The cases of one-shot and repeated games are presented. In the latter situation, coalitions are assumed to move from a strategy to another one under the constraint that they are adjacent in the graph. We introduce novel concepts of pure and mixed equilibria which are comparable with classical Nash and Berge equilibria. A Folk Theorem for G-games of repeated type is presented. Moreover, equilibria are proven to be described through suitably defined Markov Chains, hence leading to a constrained Monte Carlo Markov Chain procedure.

math.PR↗

arXiv2017

Stochastic Ising model with flipping sets of spins and fast decreasing temperature

This paper deals with the stochastic Ising model with a temperature shrinking to zero as time goes to infinity. A generalization of the Glauber dynamics is considered, on the basis of the existence of simultaneous flips of some spins. Such dynamics act on a wide class of graphs which are periodic and embedded in $\mathbb{R}^d$. The interactions between couples of spins are assumed to be quenched i.i.d. random variables following a Bernoulli distribution with support $\{-1,+1\}$. The specific problem here analyzed concerns the assessment of how often (finitely or infinitely many times, almost surely) a given spin flips. Adopting the classification proposed in \cite{GNS}, we present conditions in order to have models of type $\mathcal{F}$ (any spin flips finitely many times), $\mathcal{I}$ (any spin flips infinitely many times) and $\mathcal{M}$ (a mixed case). Several examples are provided in all dimensions and for different cases of graphs. The most part of the obtained results holds true for the case of zero-temperature and some of them for the cubic lattice $\mathbb{L}_d=(\mathbb{Z}^d, \mathbb{E}_d)$ as well.

math.PR↗

arXiv2015

One-dimensional infinite memory imitation models with noise

In this paper we study stochastic process indexed by $\mathbb {Z}$ constructed from certain transition kernels depending on the whole past. These kernels prescribe that, at any time, the current state is selected by looking only at a previous random instant. We characterize uniqueness in terms of simple concepts concerning families of stochastic matrices, generalizing the results previously obtained in De Santis and Piccioni (J. Stat. Phys., 150(6):1017--1029, 2013).

math.PR↗

arXiv2014

Relations Between Stochastic Orderings and generalized Stochastic Precedence

The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence and analyze its relations with the notions of stochastic ordering. Such a study leads us to introducing some special classes of bivariate copulas. Motivations for our study can arise from different fields. In particular we consider the frame of Target-Based Approach in decisions under risk. This approach has been mainly developed under the assumption of stochastic independence between "Prospects" and "Targets". Our analysis concerns the case of stochastic dependence.

math.PR↗

arXiv2014

Stochastic Comparisons between hitting times for Markov Chains and words' occurrences

We develop some sufficient conditions for the stochastic ordering between hitting times, in a fixed state, for two Markov chains. In particular, we focus attention on the so called \emph{skip-free} case. In the analysis of such a case, we develop a special type of coupling. We also compare different types of relations between two, non-necessarily skip-free, Markov chains on the same state space. Such relations have a natural role in establishing the usual and the asymptotic stochastic ordering between the probability distributions of hitting times. Finally, we present some discussions and examples related with words' occurrences.

math.PR↗