Related papers: Product type potential on the $X\,Y$ model: select…
In this paper we study aspects of the ergodic theory of the geodesic flow on a non-compact negatively curved manifold. It is a well known fact that every continuous potential on a compact metric space has a maximizing measure.…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
Systems of particles interacting via inverse-power law potentials have an invariance with respect to changes in length and temperature, implying a correspondence in the dynamics and thermodynamics between different `isomorphic' sets of…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
We exhibit Lipschitz (and hence H\"older) potentials on the full shift $\{0,1\}^{\mathbb{N}}$ such that the associated Gibbs measures fail to converge as the temperature goes to zero. Thus there are "exponentially decaying" interactions on…
We present the first calculation of the Bayesian evidence for different prototypical single field inflationary scenarios, including representative classes of small field and large field models. This approach allows us to compare…
We provide sufficient conditions for revenue maximization in a two-good monopoly where the buyer's values for the items come from independent (but not necessarily identical) distributions over bounded intervals. Under certain distributional…
Recommendations based on behavioral data may be faced with ambiguous statistical evidence. We consider the case of association rules, relevant e.g.~for query and product recommendations. For example: Suppose that a customer belongs to…
Depending on context, the term entropy is used for a thermodynamic quantity, a~measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in…
The theory of glassy fluctuations can be formulated in terms of disordered effective potentials. While the properties of the average potentials are well understood, the study of the fluctuations has been so far quite limited. Close to the…
Let $(X,Y)$ be a bivariate random vector. The estimation of a probability of the form $P(Y\leq y \mid X >t) $ is challenging when $t$ is large, and a fruitful approach consists in studying, if it exists, the limiting conditional…
We consider the Gaussian beta-ensemble when $\beta$ scales with $n$ the number of particles such that $\displaystyle{{n}^{-1}\ll \beta\ll 1}$. Under a certain regime for $\beta$, we show that the largest particle satisfies a large…
Warm inflationary universe models in the context of a Chaplygin gas equation are studied. General conditions required for these models to be realizable are derived and discussed. By using a chaotic potential we develop models for a…
We consider the probability distribution of large deviations in the spin-glass free energy for the Sherrington-Kirkpatrick mean field model, i.e. the exponentially small probability of finding a system with intensive free energy smaller…
An $XY$ model, generalized by inclusion of up to an infinite number of higher-order pairwise interactions with an exponentially decreasing strength, is studied by spin-wave theory and Monte Carlo simulations. At low temperatures the model…
We present a methodology for representing probabilistic relationships in a general-equilibrium economic model. Specifically, we define a precise mapping from a Bayesian network with binary nodes to a market price system where consumers and…
Warm inflation scenarios are studied with the dissipative coefficient computed in the equilibrium approximation. Use is made of the analytical expressions available in the low temperature regime with focus on the possibility of achieving…
Temperature is a widely used hyperparameter in various tasks involving neural networks, such as classification or metric learning, whose choice can have a direct impact on the model performance. Most of existing works select its value using…
Consider a topologically transitive unilateral countable Markov shift $\Sigma$, a locally constant potential $\phi : \Sigma \to \mathbb{R}$ satisfying suitable conditions, and assume that $\mu_t$ is the unique stationary Markov equilibrium…
In the context of open inflation, we calculate the probability distribution for the density parameter $\Omega$. A large class of two field models of open inflation do not lead to infinite open universes, but to an ensemble of inflating…