arXiv subjects

Subhadip Dey

Publications and source records attributed to Subhadip Dey.

At least 19 recordsLinked to original sources

arXiv2026

On some aspects of discrete groups acting ergodically on the boundary

We show that if $G$ is a real semisimple Lie group and $\Gamma 2$. The examples arise from lattices $\Gamma<H= SO(n,1)$ and their deformations in $G$. Perhaps more importantly, we describe a new approach to studying deformations of such lattices by relating them to deformations of the smooth right-translation action of $SO(n-1,1)$ on $\Gamma\backslash H$. This correspondence allows us to apply recent results of DeWitt and Dolgopyat on smooth group actions and to give examples where the right-translation action of $SO(n-1,1)$ on $\Gamma\backslash H$ can fail to be $C^0$-locally rigid.

math.DS↗

arXiv2026

Directional growth of coamenable normal subgroups: counterexamples and rigidity

Roblin's theorem asserts that, in rank one, a coamenable normal subgroup has the same critical exponent as its ambient group. Natural higher-rank analogues would predict that coamenability preserves the limit cone and the growth indicator. We show that both assertions fail, even when the quotient is infinite cyclic. For every odd integer $n\geq 3$, we construct a nonempty open family of Zariski-dense Borel--Anosov Schottky subgroups of $\mathrm{SL}_n(\mathbb R)$ admitting cocyclic normal subgroups with strictly smaller limit cones. Moreover, in $\mathrm{SL}_3(\mathbb R)$, we construct cocyclic pairs with the same limit cone but distinct growth indicators at an interior direction. We then identify the precise rigidity that survives. Let $\Gamma$ be a Zariski-dense Borel--Anosov subgroup of a connected semisimple real algebraic group, and let $N\lhd\Gamma$ be coamenable. Then the growth indicators of $N$ and $\Gamma$ agree on the fixed-point set of the opposition involution, and their Riemannian critical exponents are equal. The examples with equal limit cones show that the restriction to opposition-invariant directions is sharp.

math.GR↗

arXiv2026

Estimation of Fish Catch Using Sentinel-2, 3 and XGBoost-Kernel-Based Kernel Ridge Regression

Oceanographic factors, such as sea surface temperature and upper-ocean dynamics, have a significant impact on fish distribution. Maintaining fisheries that contribute to global food security requires quantifying these connections. This study uses multispectral images from Sentinel-2 MSI and Sentinel-3 OLCI to estimate fish catch using an Extreme Gradient Boosting (XGBoost)-kernelized Kernel Ridge Regression (KRR) technique. According to model evaluation, the XGBoost-KRR framework achieves the strongest correlation and the lowest prediction error across both sensors, suggesting improved capacity to capture nonlinear ocean-fish connections. While Sentinel-2 MSI resolves finer-scale spatial variability, emphasizing localized ecological interactions, Sentinel-3 OLCI displays smoother spectral responses associated with poorer spatial resolution. By supporting sustainable ecosystem management and strengthening satellite-based fisheries assessment, the proposed approach advances SDGs 2 (Zero Hunger) and 14 (Life Below Water).

physics.app-ph↗

arXiv2025

Fractal closures of geodesic planes in Hitchin manifolds

Ratner's theorem implies topological rigidity of immersed totally geodesic subspaces of noncompact type in finite-volume locally symmetric spaces. In higher rank and infinite volume, however, counter-examples to this rigidity have remained elusive. We construct the first such examples using \emph{floating geodesic planes}. Specifically, we exhibit a Zariski-dense Hitchin surface group $\Gamma < \mathrm{SL}_3(\mathbb{R})$ such that the Hitchin manifold $\Gamma \backslash \mathrm{SL}_3(\mathbb{R}) / \mathrm{SO}(3)$ contains immersed floating geodesic planes whose closures are fractal, with non-integer Hausdorff dimensions accumulating at $2$. Moreover, $\Gamma$ can be chosen inside $\mathrm{SL}_3(\mathbb{Z})$.

math.GT↗

arXiv2025

Anosov representations of amalgams

For uniform lattices $\Gamma$ in rank 1 Lie groups, we construct Anosov representations of virtual doubles of $\Gamma$ along certain quasiconvex subgroups. We also show that virtual HNN extensions of these lattices over some cyclic subgroups admit Anosov embeddings. In addition, we prove that for any Anosov subgroup $\Gamma$ of a real semisimple linear Lie group $\mathsf{G}$ and any infinite abelian subgroup $\mathrm{H} $ of $ \Gamma$, there exists a finite-index subgroup $\Gamma' $ of $ \Gamma$ containing $\mathrm{H}$ such that the double $\Gamma' *_{\mathrm{H}} \Gamma'$ admits an Anosov representation, thereby confirming a conjecture of [arXiv:2112.05574]. These results yield numerous examples of one-ended hyperbolic groups that do not admit discrete and faithful representations into rank 1 Lie groups but do admit Anosov embeddings into higher-rank Lie groups.

math.GR↗

arXiv2024

Deformations of Anosov subgroups: Limit cones and Growth indicators

Let $G$ be a connected semisimple real algebraic group. We prove that limit cones vary continuously under deformations of Anosov subgroups of $G$ under a certain convexity assumption, which turns out to be necessary. We apply this result to the notion of sharpness for the action of a discrete subgroup on a non-Riemannian homogeneous space. Finally, we show that, within the space of Anosov representations, the growth indicator, the critical exponents, and the Hausdorff dimension of limit sets (with respect to an appropriate non-Riemannian metric) all vary continuously.

math.GT↗

arXiv2024

Rigidity of convex co-compact diagonal actions

Kleiner-Leeb and Quint showed that convex subsets in higher-rank symmetric spaces are very rigid compared to rank 1 symmetric spaces. Motivated by this, we consider convex subsets in products of proper CAT(0) spaces $X_1\times X_2$ and show that for any two convex co-compact actions $\rho_i(\Gamma)$ on $X_i$, where $i=1, 2$, if the diagonal action of $\Gamma$ on $X_1\times X_2$ via $\rho=(\rho_1, \rho_2)$ is also convex co-compact, then under a suitable condition, $\rho_1(\Gamma)$ and $\rho_2(\Gamma)$ have the same marked length spectrum.

math.GT↗

arXiv2024

Target Characteristics on Rotation in Euclidean Space Using Full Polarimetric SAR Data

In radar polarimetry, the target characteristics significantly depend on the rotation of the target concerning the radar line of sight. Hence, several attempts have been made in the literature to compensate for the rotational dependency or to derive a complete roll-invariant parameter using full polarimetric SAR data. However, the degree of dependency of the targets on the rotation domain has yet to be well explored. Hence, in this study, we have proposed a new parameter that characterizes the targets concerning rotation in Euclidean space. The parameter shows similar values for the targets, which can be related to each other through a unitary transformation. The advantage of this parameter has been demonstrated over different canonical targets. Further, the characteristics of the natural targets have been shown using the Single Look Complex data of C band Radarsat-2 and ALOS PALSAR over the San Francisco Bay area and Cuba, respectively.

physics.app-ph↗

arXiv2024

Remarks on discrete subgroups with full limit sets in higher rank Lie groups

We show that real semi-simple Lie groups of higher rank contain (infinitely generated) discrete subgroups with full limit sets in the corresponding Furstenberg boundaries. Additionally, we provide criteria under which discrete subgroups of $G = \operatorname{SL}(3,\mathbb{R})$ must have a full limit set in the Furstenberg boundary of $G$. In the appendix, we show the the existence of Zariski-dense discrete subgroups $\Gamma$ of $\operatorname{SL}(n,\mathbb{R})$, where $n\ge 3$, such that the Jordan projection of some loxodromic element $\gamma \in\Gamma$ lies on the boundary of the limit cone of $\Gamma$.

math.GT↗

arXiv2024

Prediction of soil fertility parameters using USB-microscope imagery and portable X-ray fluorescence spectrometry

This study investigated the use of portable X-ray fluorescence (PXRF) spectrometry and soil image analysis for rapid soil fertility assessment, with a focus on key indicators such as available boron (B), organic carbon (OC), available manganese (Mn), available sulfur (S), and the sulfur availability index (SAI). A total of 1,133 soil samples from diverse agro-climatic zones in Eastern India were analyzed. The research integrated color and texture features from microscopic soil images, PXRF data, and auxiliary soil variables (AVs) using a Random Forest model. Results showed that combining image features (IFs) with AVs significantly improved prediction accuracy for available B (R2 = 0.80) and OC (R2 = 0.88). A data fusion approach, incorporating IFs, AVs, and PXRF data, further enhanced predictions for available Mn and SAI, with R2 values of 0.72 and 0.70, respectively. The study highlights the potential of integrating these technologies to offer rapid, cost-effective soil testing methods, paving the way for more advanced predictive models and a deeper understanding of soil fertility. Future work should explore the application of deep learning models on a larger dataset, incorporating soils from a wider range of agro-climatic zones under field conditions.

eess.IV↗

arXiv2024

Ahlfors regularity of Patterson-Sullivan measures of Anosov groups and applications

For all Zarski dense Anosov subgroups of a semisimple real algebraic group, we prove that their limit sets are Ahlfors regular for intrinsic conformal premetrics. As a consequence, we obtain that a Patterson-Sullivan measure is Ahlfors regular (and hence equal to the Hausdorff measure) if and only if the associated linear form is symmetric. We also discuss several applications, including analyticity of $(p,q)$-Hausdorff dimensions on the Teichm\"uller spaces, new upper bounds on the growth indicator, and $L^2$-spectral properties of associated locally symmetric manifolds.

math.GR↗

arXiv2023

Restrictions on Anosov subgroups of Sp(2n,R)

Let $n\in\mathbb{N}$ and let $\Theta \subset \{1,\dots,n\}$ be a non-empty subset. We prove that if $\Theta$ contains an odd integer, then any $P_\Theta$-Anosov subgroup of ${\rm Sp}(2n,\mathbb{R})$ is virtually isomorphic to a free group or a surface group. In particular, any Borel Anosov subgroup of ${\rm Sp}(2n,\mathbb{R})$ is virtually isomorphic to a free or surface group. On the other hand, if $\Theta$ does not contain any odd integers, then there exists a $P_\Theta$-Anosov subgroup of ${\rm Sp}(2n,\mathbb{R})$ which is not virtually isomorphic to a free or surface group. We also exhibit new examples of maximally antipodal subsets of certain flag manifolds; these arise as limit sets of rank $1$ subgroups.

math.GT↗

arXiv2023

Klein-Maskit combination theorem for Anosov subgroups: Amalgams

The classical Klein-Maskit combination theorems provide sufficient conditions to construct new Kleinian groups using old ones. There are two distinct but closely related combination theorems: The first deals with amalgamated free products, whereas the second deals with HNN extensions. This article gives analogs of both combination theorems for Anosov subgroups.

math.GR↗

arXiv2022

On Borel Anosov subgroups of ${\rm SL}(d,\mathbb{R})$

We study the antipodal subsets of the full flag manifolds $\mathcal{F}(\mathbb{R}^d)$. As a consequence, for natural numbers $d \ge 2$ such that $d\ne 5$ and $d \not\equiv 0,\pm1 \mod 8$, we show that Borel Anosov subgroups of ${\rm SL}(d,\mathbb{R})$ are virtually isomorphic to either a free group or the fundamental group of a closed hyperbolic surface. This gives a partial answer to a question asked by Andr\'es Sambarino. Furthermore, we show restrictions on the hyperbolic spaces admitting uniformly regular quasi-isometric embeddings into the symmetric space $X_d$ of ${\rm SL}(d,\mathbb{R})$.

math.GT↗

arXiv2022

Complex hyperbolic Kleinian groups of large critical exponents

In this article, we show that there exist discrete isometry groups of the $2$- and $3$-dimensional complex hyperbolic spaces with critical exponents arbitrarily close to but strictly smaller than the maximum possible value. This result shows no gap in the values of critical exponents for complex hyperbolic Kleinian groups.

math.GT↗

arXiv2022

Klein-Maskit combination theorem for Anosov subgroups: Free products

We prove a generalization of the classical Klein-Maskit combination theorem, in the free product case, in the setting of Anosov subgroups. Namely, if $\Gamma_A$ and $\Gamma_B$ are Anosov subgroups of a semisimple Lie group $G$ of noncompact type, then under suitable topological assumptions, the group generated by $\Gamma_A$ and $\Gamma_B$ in $G$ is again Anosov, and is naturally isomorphic to the free product $\Gamma_A*\Gamma_B$. Such a generalization was conjectured in our previous article with Bernhard Leeb (arXiv:1805.07374).

math.GR↗

arXiv2022

Dual Approaches to Express the Generalized Degree of Polarimetric Purity

The degree of polarimetric purity is an invariant dimensionless quantity that characterizes the closeness of a polarization state of a wave to a pure state and is related to the Von Neumann entropy. The polarimetric purity of a plane wave characterized by the second-order statistics (i.e., the covariance matrix) is uniquely described by the degree of polarization. However, the 2D formalism is only applicable when the wave propagation direction is fixed. This assumption is typical in optical and radar polarimetric measurements. Therefore, one must consider all the components to describe the general state of wave polarization. Starting from Samson and Barakat, several different concepts have been proposed in the literature to describe the 3D degree of polarization. We discuss two new ways of achieving such description: by the Coefficient of Variation and by a Direct Sum Decomposition.

physics.class-ph↗

arXiv2020

A note on complex-hyperbolic Kleinian groups

Let $\Gamma$ be a discrete group of isometries acting on the complex hyperbolic $n$-space $\mathbb{H}^n_\mathbb{C}$. In this note, we prove that if $\Gamma$ is convex-cocompact, torsion-free, and the critical exponent $\delta(\Gamma)$ is strictly lesser than $2$, then the complex manifold $\mathbb{H}^n_\mathbb{C}/\Gamma$ is Stein. We also discuss several related conjectures.

math.GR↗