Probability Papers of the Week

We study Gaussian fluctuations, moderate and large deviations around the high-density hydrodynamic limit of critical and nearly critical space-time Hawkes processes initialized by a prescribed Poisson field of past events, with no subsequent immigration.

We study connectivity, component geometry, and random walks throughout the regime $\log n\ll m<n/2$.

We study polynuclear growth (PNG) on the half-line with Poisson nucleations in the bulk and at the boundary.

We show that the vacuum partition function of the $q$-deformed oscillator \[ L_q(z):= \langle0|e^{zT_q}|0\rangle, \qquad T_q := \mathsf{a}_q + \mathsf{a}_q^* \] satisfies the Lee-Yang property, i.e., all zeros of $L_q$ lie on the imaginary line for all $q\in[-1, 1)$, proving the conjectures of Okuyama'23.

We consider a family of nonlinear Schrödinger equations with odd-power nonlinearities and fractional dispersion in an energy-critical/supercritical regime.

We determine the least $m$ for which every point of each arc occurs as an eigenvalue in our family.

In this paper, we prove that the uniform spanning tree of $\mathbb Z^4$, seen from the origin, converges locally to an infinite spatial Brownian Kesten tree: a Brownian spine onto which independent spatial Brownian trees are grafted at a constant rate.

For general sampling and counting algorithms, we establish a robust fine-grained reduction from SAT without assuming a lower bound on SAT's running time.

Near the neutral fixed point of an intermittent map, a single entrance into a small target can be followed by a long run of consecutive visits, so the number of visits need not follow its mean. We study targets $[0,u_n]$ for iid random compositions of Liverani-Saussol-Vaienti maps with a bounded parameter law that is regularly varying at its minimum $\alpha\in(0,1)$; this includes a single map.

We evaluate policies by their approximation ratio against a fluid benchmark, the optimal value of a linear-programming relaxation that upper bounds the expected net value of every policy. Under a general position gap (GPG) condition, which requires the unique optimal dual solution of this linear program to remain optimal under small perturbations of the arrival rates, we propose a longest-queue policy.

In this paper, we study the graph shotgun assembly problem in the labeled lattice model, as introduced by Mossel and Ross (2019).

We consider here the critical random-cluster model (or FK-percolation) on a large class of graphs --- namely bi-periodic isoradial graphs --- with cluster-weight~$q \in [1,4]$.

We consider mixing for a scalar advected by random vector fields, such as solutions to stochastic fluid equations.

However, existing methods that combine artificial neural networks (ANNs) with the Wiener process have not yet fully exploited the modeling power of neural networks or the analytical tractability of stochastic processes. To overcome this limitation, this paper proposes an ANN-supported Wiener process with random effects for RUL prediction.

Our main contribution is a stochastic Feynman-Kac representation for the solution, which expresses the random field as the product of the exponential martingale of the jump noise and an expectation over the paths of an independent Brownian motion.

We prove that in rotationally invariant first-passage percolation on $\mathbb{R}^d$ with $d\geq2$, the passage time $T_n$ over a distance $n$ satisfies $\mathbb{E}[\exp(|T_n-\mu n|/n^{\frac{1}{2}(1-\varepsilon)})]\leq C$ for some $\varepsilon>0$, where $\mu$ is the time constant.

We study natural exponential families whose generalized variance, the determinant of the covariance matrix, is log-affine in the natural parameter.

We provide the first mathematical construction of the non-Abelian Yang-Mills-Higgs measure on a two-dimensional torus by implementing Parisi and Wu's ``stochastic quantisation'' procedure.

We develop a theory of generalized Wishart processes within the framework of $G$-expectation, with $G$-Dyson Brownian motion and the $G$-Wishart process as two typical examples.