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The deconfinement phase transition at high baryon densities and low temperatures evades a direct investigation by means of lattice gauge calculations. In order to make this regime of QCD accessible by computer simulations, two proposal are…
In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground…
We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase…
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
Spatial prediction tasks are key to weather forecasting, studying air pollution impacts, and other scientific endeavors. Determining how much to trust predictions made by statistical or physical methods is essential for the credibility of…
We study the susceptibility propagation, a message-passing algorithm to compute correlation functions. It is applied to constraint satisfaction problems and its accuracy is examined. As a heuristic method to find a satisfying assignment, we…
We study the dynamics of condensation for a stochastic continuous mass transport process defined on a one-dimensional lattice. Specifically we introduce three different variations of the truncated random average process. We generalize…
Here we investigate the single-layer linearized perceptron near the SAT-UNSAT transition point as a prototypical model of the convex continuous satisfaction problems. The simplicity of the model allows us to take into account the effects of…
We consider the random regular $k$-NAE-SAT problem with $n$ variables each appearing in exactly $d$ clauses. For all $k$ exceeding an absolute constant $k_0$, we establish explicitly the satisfiability threshold $d_*=d_*(k)$. We prove that…
In the last three decades, powerful computer-assisted techniques have been developed in order to validate a posteriori numerical solutions of semilinear elliptic problems of the form $\Delta u +f(u,\nabla u) = 0$. By studying a well chosen…
Many NP-complete constraint satisfaction problems appear to undergo a "phase transition'' from solubility to insolubility when the constraint density passes through a critical threshold. In all such cases it is easy to derive upper bounds…
Phase transition in the two-dimensional $q$-state Potts model with random ferromagnetic couplings in the large-q limit is conjectured to be described by the isotropic version of the infinite randomness fixed point of the random…
Gaussian belief propagation (BP) has been widely used for distributed inference in large-scale networks such as the smart grid, sensor networks, and social networks, where local measurements/observations are scattered over a wide…
Conformal prediction provides distribution-free prediction sets with guaranteed marginal coverage. However, in split conformal prediction this guarantee is training-conditional only in expectation: across many calibration draws, the average…
The runtime performance of modern SAT solvers on random $k$-CNF formulas is deeply connected with the 'phase-transition' phenomenon seen empirically in the satisfiability of random $k$-CNF formulas. Recent universal hashing-based approaches…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
We consider the problem of distribution-free conditional predictive inference. Prior work has established that achieving exact finite-sample control of conditional coverage without distributional assumptions is impossible, in the sense that…
We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these…
Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from training to testing stages while the…