Related papers: Description of random fields by systems of conditi…
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
In the last few years several new Random Matrix Models have been proposed and studied. They have found application in various different contexts, ranging from the physics of mesoscopic systems to the chiral transition in lattice gauge…
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating…
We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance…
Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for…
This is the first in a series of two works which study the discrete Gaussian free field on the binary tree when all leaves are conditioned to be positive. In this work, we obtain sharp asymptotics for the probability of this "hard-wall…
Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C,…
We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…
We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative…
This survey article describes a method for choosing uniformly at random from any finite set whose objects can be viewed as constituting a distributive lattice. The method is based on ideas of the author and David Wilson for using ``coupling…
Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable.…
Self-similarity of systems is very popular and intensively developing field during last decades. To this field belong so-called stable distributions and their generalization. In Klebanov and Sl\'amov\'a (2014) there was given an approach to…
In our recent work \cite{StojnicHopBnds10} we looked at a class of random optimization problems that arise in the forms typically known as Hopfield models. We viewed two scenarios which we termed as the positive Hopfield form and the…
The purpose of this work is to expand and clarify the concept of the class of Gibbs random fields and give its structure the form accepted in the theory of random processes. It is possible thanks to the proposed purely probabilistic…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be…
In this article we study control problems with systems that are governed by ordinary differential equations whose vector fields depend linearly in the time derivatives of some components of the control. The remaining components are…