Related papers: Multiple SLE$_\kappa$ from CLE$_\kappa$ for $\kapp…
The logic $\mathcal L^1_\kappa$ was introduced by Shelah in [3]. In [4], he proved that for a strongly compact cardinal $\kappa$, it admits the following algebraic characterization: two structures are $\mathcal L^1_\kappa$-equivalent if and…
The current paper answers an open question of abs/1007.2426 We say that a countable model M characterizes an infinite cardinal kappa, if the Scott sentence of M has a model in cardinality kappa, but no models in cardinality kappa plus. If M…
We consider the coulomb gas model on the upper half plane with different boundary conditions, namely Drichlet, Neuman and mixed. We related this model to SLE($\kappa,\rho$) theories. We derive a set of conditions connecting the total charge…
This paper investigates the expected excess risk of in-context learning (ICL) for multiclass classification. We formalize each task as a sequence of labeled examples followed by a query input; a pretrained model then estimates the query's…
Square-kappa-finite, the finite family version of weak square, holds at all cardinals kappa in the Mitchell-Steel inner models.
We prove that some natural "outside" property is equivalent (for a first order class) to being stable. For a model, being resplendent is a strengthening of being kappa-saturated. Restricting ourselves to the case kappa > |T| for…
Motivated by various applications, we describe the scaling limits of bivariate Markov chains $(X,J)$ on $\mathbb Z_+ \times \{1,\ldots,\kappa\}$ where $X$ can be viewed as a position marginal and $\{1,\ldots,\kappa\}$ is a set of $\kappa$…
In this paper we analyze the connection between some properties of partially strongly compact cardinals: the completion of filters of certain size and instances of the compactness of $\mathcal{L}_{\kappa,\kappa}$. Using this equivalence we…
We investigate a class of weighted planar stochastic lattice (WPSL1) created by random sequential nucleation of seed from which a crack is grown parallel to one of the sides of the chosen block and ceases to grow upon hitting another crack.…
Every 4-connected graph with minimum degree $\delta$ and connectivity $\kappa$ either has a cycle of length at least $4\delta-2\kappa$ or has a dominating cycle.
The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated…
A cardinal kappa is countably closed if mu^omega < kappa whenever mu < kappa. Assume that there is no inner model with a Woodin cardinal and that every set has a sharp. Let K be the core model. Assume that kappa is a countably closed…
For $\kappa>0$ and $\rho>-2$, we construct a $\sigma$-finite measure, called a rooted SLE$_\kappa(\rho)$ bubble measure, on the space of curves in the upper half plane $\mathbb H$ started and ended at the same boundary point, which…
We consider the Schramm-Loewner evolution (SLE$_\kappa$) with $\kappa=4$, the critical value of $\kappa > 0$ at or below which SLE$_\kappa$ is a simple curve and above which it is self-intersecting. We show that the range of an SLE$_4$…
We develop a theory of multiple radial SLE(0) -- a smooth system of curves in a simply connected domain $\Omega$ with marked boundary points $z_1, \ldots, z_n \in \partial \Omega$ and a marked interior point $q$ -- arising as the…
We consider multiple radial SLE curves with various time parameterizations and possible spiraling behavior. We construct them by tilting independent radial SLEs with a suitable local martingale, generalizing the earlier construction by…
We apply the method of correlation functions to the coefficient problem in stochastic geometry. In particular, we give a proof for some universal patterns conjectured by M. Zinsmeister for the second moments of the Taylor coefficients for…
Constrained clustering has been well-studied for algorithms such as $K$-means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode…
We introduce a new kind of infinitary logic that we call Boolean expansion of ${\mathcal L}_{\kappa \kappa}$. This logic involves a new kind of variable, that we call generalised Boolean variable. These variables range over the powerset of…
In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. In this paper, we introduce the concept of multivariate discrete copulas, discuss their…