相关论文: The interchange process with reversals on the comp…

The zigzag process is a variant of the telegraph process with position dependent switching intensities. A characterization of the $L^2$-spectrum for the generator of the one-dimensional zigzag process is obtained in the case where the…

The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…

Bootstrap percolation on a graph iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product measure, and we say that spanning…

We give a procedure that can be used to automatically satisfy invariants of a certain shape. These invariants may be written with the operations intersection, composition and converse over binary relations, and equality over these…

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…

We introduce a new model of preferential attachment with fitness, and establish a time reversed duality between the model and a system of branching-coalescing particles. Using this duality, we give a clear and concise explanation for the…

We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…

We resolve a long-standing conjecture of Wilson (2004), reiterated by Oliveira (2016), asserting that the mixing-time of the unit-rate Interchange Process on the $n$-dimensional hypercube is of order $n$. This follows from a sharp…

The thermodynamics of the lattice model of intercalation of ions in crystals is considered in the mean field approximation. Pseudospin formalism is used for the description of interaction of electrons with ions and the possibility of…

We present a large-deviations/thermodynamic approach to the classic problem of percolation on the complete graph. Specifically, we determine the large-deviation rate function for the probability that the giant component occupies a fixed…

We improve on the abstract estimate obtained in Part 1 by assuming that there are constraints imposed by `overlapping momentum loops'. These constraints are active in a two dimensional, weakly coupled fermion gas with a strictly convex…

We propose a general Langevin equation describing the universal properties of synchronization transitions in extended systems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits,…

We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic…

In order to make argumentation-based inference contestable, it is crucial to explain what changes can achieve a desired (instead of the contested) inference result. To this end, we introduce strength change explanations for quantitative…

A graph is $H$-free if it contains no induced subgraph isomorphic to $H$. We prove new complexity results for the two classical cycle transversal problems Feedback Vertex Set and Odd Cycle Transversal by showing that they can be solved in…

We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…

We prove the existence of non-trivial phase transitions for the intersection of two independent random interlacements and the complement of the intersection. Some asymptotic results about the phase curves are also obtained. Moreover, we…

We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…

We consider the extinction time of the contact process on increasing sequences of finite graphs obtained from a variety of random graph models. Under the assumption that the infection rate is above the critical value for the process on the…